{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pyAudioKits.audio as ak"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Audio signals are divided into two categories: musical tone and noise. Among them, the musical tone is sound with a fixed pitch produced by the regular vibration of an object, while noise is the sound without a fixed pitch produced by the random vibration of an object. In this section, we are going to discuss the properties of two types of audio signals and their connection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Monotone\n",
    "\n",
    "A sine wave describes the most basic simple harmonic vibration. A sine wave whose waveform satisfies a fixed frequency and phase is a **monotone**. A monotone, in turn, is the most basic musical tone."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The power of the audio:  0.00019999999999999996\n"
     ]
    }
   ],
   "source": [
    "monotone=ak.create_Single_Freq_Audio(0.02,440,44100,1)\t#Generate a monotone with a length of 1s, an amplitude of 0.02, a frequency of 440Hz, and a sampling rate of 44100\n",
    "monotone.sound()\t#Try playing it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAEGCAYAAACpXNjrAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAAAsTAAALEwEAmpwYAABQrUlEQVR4nO29eXhkZ3ng+3urSlKV1tLeWlqt3u22sdt22yzGbF4wGYJJAgMkk5hcwJkbPCEhGa65kwBDhgnMzQ0JM9zMOCxxMqwhIXYGg8cbiw1e2nbbbru73ep2a63WXqWtqlTLd/8450hlWWqVpLPr/J6nHlWdOstXR+f93uV7v/cTpRQBAQEBAQFmEnK6AQEBAQEB/iNQLgEBAQEBphMol4CAgIAA0wmUS0BAQECA6QTKJSAgICDAdCJON8ANtLS0qN7eXqebERAQEOApnnrqqQmlVOtq3wXKBejt7eXo0aNONyMgICDAU4hI/1rfBWGxgICAgADTCZRLQEBAQIDpBMolICAgIMB0AuUSEBAQEGA6gXIJCAgICDAdR5WLiNwsIqdEpE9E7ljl+yoR+Y7+/eMi0qtvv1FEnhKR5/W/bys55ip9e5+IfElExMafFBAQEBCAg8pFRMLAl4F3AIeAD4jIoRW7fQiYVkrtA74IfEHfPgH8slLqNcCtwN+XHPPXwEeA/frrZst+REBAQEDAqjjpuVwD9CmlziqlFoFvA7es2OcW4C79/feA60VElFLPKKVG9O0vADHdy+kA6pVSjyltLYG/A95t+S/ZAn1jc9z50zP8vG/C6aa4htlMjm883s93jw6SzRecbo4rUErx4IlRvvKzswwn0043xzX0jc1q8nMmkB+DGV1+/uHoIJmcc/Lj5CTKLmCw5PMQ8Nq19lFK5UUkBTSjeS4GvwY8rZTKikiXfp7Sc3atdnERuQ24DaCnp2cLP2Pz/PjUGLf9/VMs5osAfOz6/fzBjQccaYtbmJjL8r7/8QvOjM8D8I3H+vnWba+junL7zvdVSvEf/vk433x8AIC/uP8lvvHh13JFT6PDLXOWh0+N8Tt/9xSLBU1+fv+G/fz+Ddtbfibnsrz3f/yCs4b8PD7ANz/yWkfkx9MD+iJyCVqo7Hc2eqxS6k6l1BGl1JHW1lWrF1jKxFyWP/jOMfa21vLTf/9Wfu3Kbv7qwdM8cnp7W2B//P3jDE6nuev/uIb/+oEreG44xed+cMLpZjnKvzyX4JuPD/CR63bzwMffTEttFbd/8xnSi9vXq5uYy/Kxbz3D/nZNfn71yi7+8oHT296DueOfnmdoOs3ff0iTn2eHkvzZvScdaYuTymUY2FnyuVvftuo+IhIBGoBJ/XM38H3gt5RSZ0r2717nnK7g/3v4DDOZPP/1A4fpaa7mc79yKT1N1fzZD09QLG7P1UGPnpviRy+c52PX7+fNB1r55cs7ufX1vXzriQH6xmadbp4j5ApFPn/vCS7tqueOd1zMvrZa/vy9lzOcTPO1R192unmO8d8e6mN+scBfvf8KTX7e/Rp2NsX4z/eeYLuurvvEy1Pc/+Iov3/Dfq7br8nPb71uF998YoCXJ+Ztb4+TyuVJYL+I7BaRSuD9wD0r9rkHbcAe4D3AQ0opJSJx4AfAHUqpR42dlVIJYEZEXqdnif0WcLfFv2PDpNI5vvlEP+8+3MW+tjoAohVh/t3b9vHCyAy/ODvpcAud4b//5CxNNZX89rW9S9t+7/r9VIRDfP3Rc461y0l+8FyCkVSGP7zxIOGQlvh4ze4m3nSgla8/em5bjkmlFnJ858lBfvWKLva11QIQqwxz+1v3cXx4hkf7tqf83PnTs7TUVvLbb9i9tO32t+0nEhL+5mdnbW+PY8pFKZUHbgfuA04A31VKvSAinxWRd+m7fRVoFpE+4OOAka58O7AP+JSIHNNfbfp3vwt8BegDzgA/tOcXlc/dx4bJ5Ip88A29r9j+y5d30lhdwTceX7MWnG8Zm8nw0MlR3nf1zlfEh5tqKrnlcCf/9PQwC4t5B1voDN96YoDdLTW8+cArQ7e/fW0vE3NZHjox5lDLnOP7zwyRzhX4YIkRAvDuK7qIV1fwnaODqx/oYxKpNA+dHOVfH9lJrDK8tL21rop3XtbJPcdGmM/aKz+Ojrkope5VSh1QSu1VSn1O3/YppdQ9+vuMUuq9Sql9SqlrlFJn9e3/SSlVo5Q6XPIa0787qpS6VD/n7cqFPvK/PDvCRTvqeE13wyu2RyvC3HK4iwdOjDGbyTnUOme459kRigree1X3q777tSu7SecK3P/iqAMtc47hZJrHX57iV6/oIhR65XSt6/a10FZXxT8948qor6Xc/ewIF3fUc0nnK+WnKhLmlss7ue+F87Z3pE7zo+PnKSp4zyry86+PdDOXzfPgSXsNEU8P6HuR6flFnuqf5qZD7at+/87LOljMF3nI5gfBaR46OcbB9jr2tNa+6rure5voaIhy7/MJB1rmHA/oyvSdl3e+6rtIOMQvvaaDn50edzTd1G5GkmmeGUjyy5d3rPr92y/dwWK+yKPbLLX/gROj7GurXVN+Wuuq+KHN8hMoF5t5+NQYRQXXX7y6crmyp5GW2kp+fGrc5pY5x2wmxxMvT/HWi9pW/T4UEt5ysJWf902S19NOtwM/eWmc3uZqdrfUrPr9mw+2kskVeeLlKZtb5hw/O63JxfUXrS4/R3Y1UVsV4eFT28c4S6VzPH52ihvW6FNCIeHGQ+385KVxcjbKT6BcbObBE2O01lXxmq6GVb8PhYQ37G3hkb6JbZP18mjfBPmi4q0H104Jv25/K7PZPM8OJe1rmINkcgV+cWbyVWMtpbx+TzNVkdC2MkR+enqCtroqDrS/2kIHqIyEuG5/Cw+fHN828vOTl8bJFxU3HlrdOAMtjLqwWODZwaRt7QqUi43kC0V++tI411/U9qoYeilv3NfC+GyW02NzNrbOOR46OUZdNMJVu9aeFPiGvc2EBH760vYIdzx5bop0rsCbL6BwoxVhXrunmZ+8tD2s9EJR8WjfBNftb+VCJQPfelEb52cynEhsj/T1H58co7mmksM715af1+9tRgRbM+kC5WIjJxKzzGbzvGFfywX3e8O+ZoBtM6HykdMTXLe/hUh47ccxXl3JZd3xpbCI3/nJqXEqwyFet6f5gvu9+UArZ8bnGZxasKllzvHCSIrkQo43Hbiw/LxF9/Ye6dsez8oT56a4ZnfTUqr6asSrK7mks55HbZxkGigXGznar8XGr+69cNmO7sZqepurt8WgZCKVZiSV4erepnX3vW5/C8cGk9sik+7Jc1Mc7omvW7bjDXs15WM8W37mEV0erl3HOGurj9LTVM3T/UkbWuUsiVSaoek0R8qQn2v3tvDMwLRtKf2BcrGRo+em6YrH6GiIrbvv6/c288S5Kd/P1jc6gCvLqJN1pLeJooLnh1IWt8pZMrkCL4zMlHVPDrTXUVMZ5pmBpPUNc5in+5PsaamhpbZq3X2v2tXIUwPTvh93OXpuGljfYAV4w74WcgXFU/3TVjcLCJSLbSilONo/dcFxhVIO74wzm8lzbtL+sg128lT/NNGKEIc669fd93B3HIBnbByUdIIXRlLki4ore+Lr7hsOCZfvjPteuSilODaY5PDOeFn7X7mrkfHZLEPT/q4g/VT/NNWVYQ51lCE/+r17zibjLFAuNjE0nWZ0JsuRMiwMgMv1B8Hv2VFPD0xzWVeciguMtxg0VFewp6WGYz5XLoY3d7gM5QJwRU+cE4kZXxeyHEllmJjLln1PrtK9vqcH7LHSneLJc1Mc3hm/4HilQUPMXvkJlItNGA95uZ7L/rY6qivDPDvo3xCQFv5JcWWZ9wQ06+vYYNLX4Y5nBqfpbozRVhcta/8rexrJFxXPD/v3WTmme2blei4Hd2jhQrtCQE6wsJjnRGKGIxuQn8u6G3jOJoM1UC42cXw4RVUkxMH2urL2D4eES7safG2lvzAyQ66guKJMaxQ0a358NstIKmNdwxzmmYHkhtZqMTpcP1vpxwanqYyEuGjH+uEf2B7hwhOJWYoKLl1jztxqXNYdZ3Qmy+iM9fITKBebeGFkhot21JXlvhpc3t3AiyMzS4uJ+Y0XRzRLe60JpathdKTP+LQjHZvNkEhluLy7/HvSXFtFT1O1rxMdjg0muaSznspI+fJzaVcDp0ZnfVvVwZCfSzYgP5fv1Pa1YzJloFxsQCnFi4mZsgatS7l8Z5zFQpGT52csapmzvJiYpSFWQUdDeeEfgIt21BMJCS+O+POeGBP/NvqsXNxRx4mEP+9Jsah4YWSGyzbQiYJ2TxbzRc46sJaJHbwwMkO8uoLODcjPoY4GwiGxZVA/UC42MJLKkFzIcahzY8JhVH31a6fxYmKGQx31F5xtvZLKSIh9bbWcPO/P2dcn9f91Odk/pVzcUc/Lk/O+HNQfnF5gYbHAxRu8J4c6NPnxqyGyGfmJVYbZ31bL8ZFAufgC4+HeaIfR01RNtCLky460UFScOr9xbw7goh11S52w3ziRmKGjIUq8unJDx13cUY9ScGrUf8+K8fxftEH52dNaQ2UkxIs+fFZyhSInz89yySbl5yUb+pRAudjACyMpRDQ3fSOEQ8KB9jpO+VC5vDwxTyZX3LA1ClonM5LKkFrw30z9E4nZTd2Ti/WBbj96uScTs4iwZrHKtagIhzjQXutLz+XM+ByL+eKr1rQph4M7dPlJWys/jioXEblZRE6JSJ+I3LHK91Ui8h39+8dFpFff3iwiD4vInIj8txXH/Fg/58oVKh3jxZEZdrfUrFvKYzUu2uFP5fLiJsM/oN0TwHdjUdl8gTPjcxs2QgC6G2PUVkX8qVzOz9DbvDn5OdRRz4nEjO9S1w2FuVnPBeAli71cx5SLiISBLwPvAA4BHxCRQyt2+xAwrZTaB3wR+IK+PQP8CfBHa5z+N1auUOkkp0ZnlyzLjXJwRz2T84uMz2ZNbpWzvDgyQ0VYltZA3wiGZe+3cGHf2Bz5otqU5xIKiR4u9Nc9Ae3/XG4K/0oOdWjyMzrjL/l5aXSOirCsudbPhTi4ZJz5VLkA1wB9SqmzSqlF4NvALSv2uQW4S3//PeB6ERGl1LxS6hE0JeNqMrkCg1MLm+pEYdnK8Jv3cnp0lj0ttRtKLTVoq6uisbrCd56LkSlW7lyOlVzsQyt9YVErgXTRJrw5gAO6/Jwe85f89I1p8rORqQ0GHQ1R6qIRTlksP04qly5gsOTzkL5t1X2UUnkgBVy4BrnG1/WQ2J/IGqkUInKbiBwVkaPj49aV5j47Pk9Rwf4NxosNDvo0BNQ3PrdphSsiHNxR57v1Ok6PzVIZDtHbXL2p4w+01zKbzfvKSn9pdA6llo2sjWI8Y30+Wxvp9Ngc+zbZp4gIB9vreOm8tffEjwP6v6GUeg1wnf76zdV2UkrdqZQ6opQ60tq69oJMW8WwmPa3bU44WmqraKmt9JXnYnhzezepXECrBnxmfM5XVvqZsXl2t9RsyhoF2Kuvn35m3D8dqaEUDmwyLNZaW0V9NOKrhfcyuQIDUwvsa928/BzcUcfJ89Z6uU4ql2FgZ8nnbn3bqvuISARoAC64lJpSalj/Owt8Ey385hh9Y3OEBHpbNmeNgmZ9+anDeHlC9+a2oFz2ttYym8kzPucfK/3M+Bx72zYeQzfwo5V+ZlwbW9jZtDn5EdHG9fx2T9QWoiGgKeuZTN7SsVwnlcuTwH4R2S0ilcD7gXtW7HMPcKv+/j3AQ+oCqlZEIiLSor+vAN4JHDe95Rugb2yO3uYaqiLhTZ9jT2stZ8bnfWOlG4K+2bAYlFjpY/6YfZ3Na9bo3i1Yo611VdRVRXxliJwZm2NXc01ZVbPXYn9bHWd8pFwM+dlsNARKvVzr5Mcx5aKPodwO3AecAL6rlHpBRD4rIu/Sd/sq0CwifcDHgaV0ZRE5B/wF8EERGdIzzaqA+0TkOeAYmufzNzb9pFU5PTa3pfAPaA9CKp1jan7RpFY5i+HNbSbTxcCw8P3SkfZPLlAoqi0pXBFhrw+t9L2tm39OQDNiJucXmfaJ/JwenSMcki1FQ/bo9/TshHXPysYTx01EKXUvcO+KbZ8qeZ8B3rvGsb1rnPYqs9q3VXKFIucm5rnpUPuWzrP8IMzTXMYqfG6nb3yOnU3VRCs2783tqI9SXRn2jXIxLOuteC7G8T877Y+143OFIgNTC7z9kh1bOs9SuHB8jqtr1l8O2O2cHptlV3P1lqIhO+qjxCrClnr+fhzQdw39k/Pkt2iNAuxt0Y4/66OOdCuDkaBb6Xq40A8Y3sYeE6z0sdksMxnvVy8YnFogV1BbVrh+G4s6Oz6/5XsSCmlzZKz0XALlYiHnJhaArYV/ALoaY1RGQr7oSAtFxdmJ+S0rXIC9rTW+iaWfGZ+jKx7b1Cz0UowQkh/ui/G8bzWs3BWPEa0I+UK5FIuK/qmFLfcpoBkyZ/045rIdODep/eN6m7f2IIRDwu7mGl94LolUmsV8kV4ThGNvay3DybQvKgGfGZ/fstcCy1a6HwwRI+S51fsSCgm7mmron1wwo1mOkpjJsJgvsmuTc6FK2dNay+D0ApmcNfITKBcLOTc5T300Qry6YsvnstrKsIsBXcDNEg6wdlDSDpRSnJuYN8Ua7W6sJiQwMOn9Z+XM2BytdVXUR7cuP7uaq+n3wT3p19em2b1FgxU0L1cpLFO6gXKxkP7JBXpbaja03sJa7G2tpX9qgZzHV9U7pz/IW/XmYFlBed0inV7IMZvNs8uEe1IZCdEZjy3dZy/TP7mw6WoFK+ltqaF/aoFi0dvp/Mb/dZdJnj9YN5YbKBcLOTc5b0onClpHWigqhqfTppzPKfon56mMhNhRX/7qeWvhF+ViWNS7NjlRcCW9zVpH6nX6p+bpaTJPfhbzRc7bsHa8lZzT5afDBPnZ3VJDd2OMRYsM1kC5WMRivsjwdNo0y6tH73i83mmcm5ynp6maUGjr3lxdtILmmkoGprwd7ug3MVQI0OODEFAmV2B0JmvaPdmlKymvGyLnJubZZZL81FRFeOT/ehu3HF5Z0tEcAuViEUPTCxQVpoQ6YPk8Ax5XLmaGOsDoSL1/T0TYdImTlfQ2V5NcyHl6MTXjOTdNuSx5ud5Wuucm503rU6wmUC4WsZQptoVZtKW01VVRFQl5eqBWKUX/5IKpwrGryQ/KZZ4d9dEtTSotxQgl9XvYozP+pz0mKdzOeIyKsHh6LKpYVKYbZ1YSKBeLMOa4mNWRhkJCj8c70vHZLOlcwTRrFKCnuWYpvdmr9E8tmHpPDIPGy89Kv0lp/AbhkFb80suey+hshqxJafx2ECgXi+ifnKeuKkJzTaVp5+xpqvZ0WGwp08Vkz6WotDCkV+mfnF8aEzCDpfE5D3ekA1ML1JmUxm/Q2+ztuS4vT5ircK0mUC4WcW5ygV0t1aakIRv0NGvKxavVkZcnlZpnpS/F0j2qdOeyeSbmFtllUvgUoLoyQltdlac7Ui18aq78GHNdvCo/Zid+WE2gXCyi34KBt11N1SwsFpiY82Z11/7JeSIhoSseM+2cPbqgDXi0I12aVGqi5wJGR+rNewKa52L2PeltrmHew/JzbnKeyrA2j8kLBMrFAnKFIoMmpiEbLGeMeTPc0T+5QFdjbNMrLa5Ga20V1ZVhz3akS3NcLHhWvDqgXygqhqYXlgwHs+jxeMbYuYl5djbFCJuQhmwHgXKxgOHpNIWiMt1z2dnk7YFaszPFQKuOrI1FebPDMMJ5Zneku5qqGZ3JerLu2kgyTa6gTJtUamCMVXg1Y0zLFPPGeAsEysUSlnL0TRaOnU0xRLypXJRSesUC8+PFXg4B9U/O01RTaUr9rFKM8iBeTAAZsEjhdsU1q9+L6fxKKQanFkybC2UHjioXEblZRE6JSJ+I3LHK91Ui8h39+8dFpFff3iwiD4vInIj8txXHXCUiz+vHfEnMHBEsk0E9c8nsB6EqEqajPsqgBzuM5EKO2UzetHkLpexqrmHAo3WjjIFrs9nl4YyxfguyCsGouxb1pOeSXMgxv1igu9Eb4y3goHIRkTDwZeAdwCHgA/pSxaV8CJhWSu0Dvgh8Qd+eAf4E+KNVTv3XwEeA/frrZvNbf2GGptNEQkK7CfV/VtLTXO3JzKghvSaaFZZXT1M12XyRsdms6ee2mv7JBdM9XPB23bX+KW3g2oz6cyvpjlcznPRefT4r5ccqnPRcrgH6lFJnlVKLwLeBW1bscwtwl/7+e8D1IiJKqXml1CNoSmYJEekA6pVSjykt3/DvgHdb+SNWY2g6TWfcmoE3r06kNOahmJkpZuDV0h75glZI0YoOoyFWQV1VxJMd6cDkAt2N1shPd2PMk3OijDYHnkt5dAGDJZ+H9G2r7qOUygMpoHmdcw6tc04AROQ2ETkqIkfHx81dc3xoesGyh2BXcw0Tc1nms3lLzm8VS5ZXo/kdqXHOIY9VjE6kMhSKyhKFKyJ0ebYjTVtmoXc3aokO2by3Eh2MZ7vbAvmxim07oK+UulMpdUQpdaS1tdXUcw9Npy3pRGHZcvGaRTo0vUBdVYT62NaW8V2NjnhUv4bX7om1HYZmpXvrnoD2rHRZZJwZ8jOS9Fbp/cFprWJBQ8zcxA8rcVK5DAM7Sz5369tW3UdEIkADMLnOObvXOaelZHIFxmezlnkuRkfktXVdhqbTdDXGTJ1xbVAVCdNeX8Vw0ltWumEgWPmsDE+nPTUjfT6bZ3ohZ+E90c7rNY/OSoPVKpxULk8C+0Vkt4hUAu8H7lmxzz3Arfr79wAPqQtIilIqAcyIyOv0LLHfAu42v+lrs9RhNAXCUcrQdNpSl74r7j0r3fgfGp6X2XTFY8xm88ykvRNCNeTHilAhQHeTV40z60LtVuGYctHHUG4H7gNOAN9VSr0gIp8VkXfpu30VaBaRPuDjwFK6soicA/4C+KCIDJVkmv0u8BWgDzgD/NCO32NgdaijtbaKynCIIQ+FxZRSDCfTlgpHd6P3soCGp9O011dRFTGn1P5KlgwRD3l0wxbLT3tdFeGQeMoQUUpZbpxZgfkB8A2glLoXuHfFtk+VvM8A713j2N41th8FLjWvlRvD6qyOUEjojEc9ZXml0jnmsnlLlUtXY4wfHk9QLCpTVumzA6s7jO6SRIdLOhssu46ZWC0/kXCIjoaopzz/6YUcCx6b4wLbeEDfKoam01SEhbY6a0IdgJ4F5B3lYkemS1c8Rq6gPDXXZSi5YFn4B1gaFPfUs5JMUxkO0VpbZdk1vJbo4MU0ZAiUi+lYOcfFoCse81QIyA7h8NpYVKGoSCQzlt6TxuoKqivDnvJyNfmJWup9djdWe0q5DE55bwIlBMrFdOwYeOuKVzM+myWT80au/rLnYr1y8YrSHZ3JkC8qS705EfHcpMFhPavQSrobY/qqjl6RH30CcuC5bG+GptN0x621MJZz9b3RkQ5Np6mtsjZHvyvurYmURjut7jC8lkVnj/xUoxQkPDLXZWg6TUOswvTiplYTKBcTMea47LQoDdmgy2NWuuHNWVlDNFYZprmm0jMdqTEnx2ov10tZdJlcgYm5rC0KF7xkiHgvDRkC5WIqy5PirLW8DOHwSixdy4qyXji8FAIamrJ2PodBd2OMVDrHTCZn6XXMwOpJpQZeG5+zS37MJlAuJmJXqGNHQ5SQeMNzsTNHv6vRO4kOw8k0LbVVRCusmeNi4KWKDkYbrVa4HQ1Rz8x1MeaIdVkcKrSCQLmYiF3CUREO0dHgjVi6HXNcDLxU7sQua3QphOqBZ2Up8cPirKiIXs5/0AOeSyqtzXHptKiKg5UEysVEEqk0IYG2Outy9A264jFPdBiGJ9FpscIF7Z5k80Um5hYtv9ZWsSuO7qUQ0HBygXBIaLdJfrwwoG8U2LRDfswmUC4mMpLM0F4fJRK2/rZ6JQRkp3B4pSMtFhUjyYwtqaXNNZVEK0KeeFaGptN0NNgjP53xqCfuSSKltbGjIfBctjWJVNo2C6MrHiORSpMrFG253mYxhKPTBuHwyoz0yflFFgtFOhusf1ZEhI6GGCMp91vpw9Npy0PKBh3xGKMz2no6bmbERs/fbALlYiIjybRtFkZ3Y4yigvMu7zRGkhkqwkKLheU8DAwBNBSaW7HbGu1oiHpiTtRI0j7l0tkQJV9UTMy5u1zQSEqTHyvL4VhFoFxMQilFIpWxzcIwruP2TiORStNeb205D4P6aAW1VRHXLwRltzXa6YHxhUJRMTqbtWz5gZUY997tobFE0j75MZtAuZjE1Pwi2XzRNmvUyB5JuNxzSSQztoR/DDoaoq73XOwepO1siDI2myHv4hDq2KwWouqw6VkxruN2pTuSsld+zCRQLiZhd4dhCMeIyzvS4WTa1jTKjnjM/Qo3laYqEqKx2p5yHh1xLYQ66uKK0cvyY8+z0uWhEKpd3pzZOKpcRORmETklIn0icscq31eJyHf07x8Xkd6S7z6pbz8lIm8v2X5ORJ4XkWMictSmn7LUydtlZdRURaiPRlxteRWKitGZDB02DkZ2NkTdHxbTw6dWlsMpxfCm3RxCXR6HsudZqY9FtIrRLr4nxaLifCpj2z0xG8cWCxORMPBl4EZgCHhSRO5RSr1YstuHgGml1D4ReT/wBeB9+qqT7wcuATqBB0TkgFLKKHP6VqXUhG0/Bi02CtYtWbsanXrGmFuZmMuSLypbMsUMOhpiTMxlyeYLlq3wuFUSNiZ+wLKV7mrlYnguNnWkWhZd1NXG2cRcllxB0RV4LhvmGqBPKXVWKbUIfBu4ZcU+twB36e+/B1wvmrl3C/BtpVRWKfUy2pLG19jU7lVJpDJURkI011Tads0Ol1vpRmdmp+VlhFVGU+4NASVstkY7lkJALn5WUmmqK8PUx+yzd91unBnp4171XJxULl3AYMnnIX3bqvsopfJACmhe51gF/G8ReUpEblvr4iJym4gcFZGj4+PjW/ohoI8tNERtC3WA+4XD6MzszNF3exZQvlBkdCZj6zhUbVWEumhkybt2I4lkhg675cfl83+ciIaYiR8H9N+olLoSeAfwURF502o7KaXuVEodUUodaW1t3fJF7bZGQetIpxdypBfduejRcsqtnWExI4vOnR3p2GyWorLfGu1siDHsYi/XzgnIBh3xKOOzWdcuGmYoviBbbOMMAztLPnfr21bdR0QiQAMweaFjlVLG3zHg+9gULksk7c/qcHtHOpLMEKsIW7pI2EqWUkxdapGOOGSNdsTdnaI9ksrYXuLEUGZuDaGOJNNEK0LEbcoqNJuylIuIHBCRB0XkuP75MhH54y1e+0lgv4jsFpFKtAH6e1bscw9wq/7+PcBDSit5ew/wfj2bbDewH3hCRGpEpE5vYw1wE3B8i+1cl3yhyPkZ+/PRl9KRXWqRGmmUdoY6YpVhGqsrXDt47ZQ12uniFO3FfJGJuawj3hy4N53f8ObslB8zKddz+Rvgk0AOQCn1HJoy2DT6GMrtwH3ACeC7SqkXROSzIvIufbevAs0i0gd8HLhDP/YF4LvAi8CPgI/qmWLtwCMi8izwBPADpdSPttLOcjBCHXa79Ua4ya3C4dQEsI4G93akCQdChaClaE/NL5LJuS8ENDqTQSn774nhPbrWELF5ArLZlJuaUa2UemKFBs1v9eJKqXuBe1ds+1TJ+wzw3jWO/RzwuRXbzgKXb7VdG2UpR99m4dhhhMXc6rkk0xw8uPXxrI3SGY+6tnhlIpWhripCnc3roS97uWn2tNbaeu31cKo4Y6fLQ6iJVJo37bdffsyiXM9lQkT2omViISLvARKWtcpjjNico29QFQnTUlvpylj6Yr7IuAOhDnB3CGjEgbE5WDZ83HhfEg6l3Lo5hJorFBmbzdo6AdlsyvVcPgrcCVwkIsPAy8C/saxVHsOpQVrAteXUnQp1gHZPUukc89k8NVWOzRNeFSeyCsHdEymXqls4JT8uvCfnU7r8eHAdF4OyJE8PN92gD5KHlFKz1jbLWxihjnqbQx2gZYy9PDFv+3XXw4kJlAbLRT3T7Gurs/36FyKRSnNpV73t110KobrQEEkkMzTEKqiutN8Q6IzHXLm43JI351fPRUQ+vsZ2AJRSf2FBmzyHU6EO0ITj52cmHbn2hVieQOmMNQpauNJNyiWTKzAxt+iIwjVCqG600hMpe8vhlNIZj/LEy26UH+3/5NXSL7C+52JI5kHgapZThX8ZLRsrAM2td6pEQ2c8ylw2z0wm54jntBYjNhciLMWt83/OL40tONNhuDWEOpK0bx2klXQ0xJjJ5JnL5ql1UQjVGMf1aukXWGdAXyn1H5VS/xFtkuKVSqk/VEr9IXAV0GNHA71AImlvOY9S3LouhRHqcGLMY0dDFBH3zf9ZHltwzhBxYwkYpz0XwHX3JZFKUx+NuG7McCOUmy3WDiyWfF7Ut217MrkCk/OLjuWju3Wui5MdRkU4RGttles8l0TSBZ5LMo02D9kdpBcLTC/kHFS4xkRKlxkiSfvL4ZhNuWrx79BmwH9f//xulqsVb2vOOzzw5lbPxclQB7gzHdnuNUtW0hmPMr9YYCaTt7Ukz4VYDp86pXDd6bmMJO0vh2M2ZXku+oTF3wam9ddvK6X+s5UN8wpLE8AcehDa6qoIifvGF0Yc9FxA60jdVhl5JJWhqaaSWKUz68ws111zz31JODy20F4fJSTuS9F2opCn2ZRbW6wHmEArBPl9YFLftu0ZcdhziYRDtNe7a12X9GKBpIOhDtBLwCQzrgoB2b1I2EqWxxfc86w4OccFtBBqW13UVWExp0OFZlFuWOwH6LPzgRiwGziFthLktmZpzQUHO42OBndVvHW6wwDtnqRzBVLpHPFq+xZwuxCJVIbuxmrHrr88vuCeZ8VQdDuclB+XVYxOOBwqNItyw2KvUUpdpr/2o5Wx/4W1TfMGI6k0zTWVRCucW1K3I+6uWcZOhzqgpCN1kZU+nEw7qnDb6qKEQ+KuZyWVpqW20tElqTvjMVc9J35IQ4ZNrueilHoaeK3JbfEkI8mM4yvFdemD124JAS15Lg4Kh9vmusxl88xm8o52GOGQ0F5X5bKwmDPlcErpbIi6KovODZ6/GZQVFlsxUz8EXAmMWNIij5FIpdnVXONoGzoaomTzRabmF2murXK0LbDsubQ3ONcWt6WYOlVqfyUd8ZjLwmJp9rQ6LT8xsvki0ws5mmqcD6G6IVRoBuV6LnUlryq0MZhbrGqUl0gkM0tFAZ3CbasvjiTTtNZVORrqaK2toiIsrkkxHXGo8u9K3Jai7VQhz1I6XVbUUwsVOis/ZlDugP6LSql/KN0gIu8F/mGN/bcFM5kcs9m84wNvnSWLHl3a1eBoW0Bz652u5hoKiZ5F55IOwwWJH6CFgO47nqFYVIRCzq5wOJPJMZfNO+7NuU9+nKv4YSblei6fLHPbhhCRm0XklIj0icgdq3xfJSLf0b9/XER6S777pL79lIi8vdxzmsnSwHXgubwCN1ijoI35uCUsNpLKIOJ8qKOjIcpiocjk/OL6O1uMGxI/Sq/vFvkZcThl3SzWq4r8DuCXgC4R+VLJV/VscSVKEQkDXwZuBIaAJ0XkHqXUiyW7fQiYVkrtE5H3A18A3icih9CWWb4E6AQeEJED+jHrndM0lgeunX0QmmsqqQyHXBFLV0qRSKa5bn+L002hIx7l6YFpp5sBaJ5LW10VFeFN5dCYhmEIJVJa6NJJ3DJw7Ub5eeM+5+Vnq6z3pI8AR4EM8FTJ6x7g7Rc4rhyuAfqUUmeVUovAt3n1OM4tLJeZ+R5wvWj1/m8Bvq2UyiqlXgb69POVc07TMCwvpyc7hULCjoaoK7KAZjJ55hcLjo9DgWaRnk9pISCncZM3B+5I0XaL5xIKiTbXxQX3xJAfpxWuGVzQc1FKPQs8KyLfUEptyVNZhS5gsOTzEK9Ob17aRymVF5EU0Kxvf2zFsV36+/XOCYCI3AbcBtDTs7liA+EQ7G6poc1hCxDcM5HS6fpZpXTGo+QKion5LG11zgrrSDLNRR3Ory3TUbKQmtMkUmlCgmvkxw3jc4klb855+dkqF/RcROS7+ttnROS5lS8b2mcZSqk7lVJHlFJHWltbN3WO913dw8N/9BYiDoc6QJvr4gZr1Mkln1fS6ZKinkopR9f8KaW5ppLKSMgV4wsjyQzt9VFXyE9ngzuy6NzizZnBetliH9P/vtOCaw8DO0s+d+vbVttnSEQiQAMwuc6x653Tl3TEo5yfyVAoKsIOZgEZCs7JCZQGpVb65TvjjrUjuZAjkyu6YpBWRFxlpbvhnoB75GfYJfOhzGC9xcIS+t/+1V5bvPaTwH4R2S0ilWgD9Pes2Oce4Fb9/XuAh5Q2jfYe4P16NtluYD/aypjlnNOXdDTEKBQV47NZR9uRSKWJhMTxwWJYVnDDDnsuTi8SthIthOoCKz2VcTzT0qAz7h75CYfE8TCuGawXFpsVkZmS12zp361cWB/DuR24DzgBfFcp9YKIfFZE3qXv9lWgWUT6gI8Dd+jHvgB8F3gR+BHwUaVUYa1zbqWdXsEti4Yl9FCHk9afQby6gmhFyPGJlE4vEraSznjM8XuilNLKyrvlniwZIs4/K+11Va6Qn62y3oC+pSOQSql7gXtXbPtUyfsM8N41jv0c8LlyzrkdeMWiYQ4uhuD0Oi6liIgrYunGIK0bMuhA60hHZ7OOhoCm9VCha7y5VyQ6NDrWjpFU2jXe3FYpeyRNRK4Ukd8TkX8nIldY2aiAjdNZMn/BSdwU6gCt03DamxtOZqgICy0uqPsG2j0pFBVjs84p3aXEDxeMzYF7VnR1egVXMyl3sbBPoc03aQZagL8VkT+2smEBG6M+GqGmMuyoW18sKhJJd5Wu6NQXDXOSRCqtrXjoklCHG+a6jLhs4Lo+GqG2KuKoIVIsKs6nMq4JFW6Vcj2X3wCuVkp9Win1aeB1wG9a16yAjSIidMSd7Ugn5xdZLBRdkSlm0BGPMTqbIVcoOtaGRDLjsnuyXEvLKRIuKeRp4IYsuiX52U6eC9pM/VJ1WsU2SfH1Ek5PpHTjCnqdDVGUgtEZB630VNoV834MlmtpOfesjCTTVEZCNLugxL1Bh8MVo0dcUtzULMpVLingBRH5WxH5OnAcSIrIl1bUHAtwkK64s4UaR1xSDqeU5VpaztyXYlExOuOuOLoRQnU0LJbK0NHgnlAhGIuGOXdP/DQ7H8ovuf99/WXwY/ObErBVOhpijM9myeYLjqwF4VbPBZwLAU3MZckVlKvi6EshVCe9XBdW/u1oiDEx55z8uNE42wplKRel1F3r7xXgNEboZTSVpae52vbrJ1IZqiIhV6zmZ+C05zLssqwoA6cnUiZSGV67u8mx66+GkVxwPpVxZHXZkWSaqkiIxuoK269tBeVmi71TRJ4RkSmzJlEGmM9SFpBDFqmxDoVWuNod1FZFqI9GHJs0uDRw7aIxF9DXunEoBFQoKs67LFQIpStSOnNfEiltVVs3yc9WKDcs9pfArwLP6+VXAlyI0xVvNeXirg4DtE7DqRIwRjjOLRMoDTrjzoWAxma1Gl5uU7hGmM4x+XFZ4sdWKXdAfxA4HigWd+P0/AVtAqX7hMPJLLpEKkOsIkxDzF2hjtIQqt24qbhpKU6vSOlW42yzlOu5fAK4V0R+Aiw9jUqpv7CkVQGbIlYZprG6wpHB63yhqGVFuVA4OuIxnh1KOXLthG6Nui3UURpCtXt8zk3LMpQSqwzTVFPpyETkXKHI2GzWdaHCrVCucvkcMIc218U9o7UBr6LDoVpaY7NZisqdmS6dDVGm5hfJ5ApEK+wNAQ27bAKlgZMhVDen3HY0RB0ZnxudyaCU80umm0m5yqVTKXWppS0JMIXOeJShaec6DLdZo/DKcMfuFnuzgBLJNAcObG4xOitxMoQ6kszoiRbuChWC9qwMTS/Yfl3j/+Cmunxbpdwxl3tF5CZLWxJgCk55Lm6No0NJUU+bLdLFfJHxOXeGOmKVYeLVFY54LiMunONi0Bl3pgTMcuVsd96XzVCucvk/gR+JSDpIRXY3nfEYqXSO+Wze1uu62XMx5i/YHUtfCnW48J6Abog44Lm4rXJ2KZ3xGDOZPHM2y8+Ij5Y3Nih3EmWdiDShrfjoTkkJAJY7skQqzb42S5fjeQVuDnXsWEoxtbcjdVtxxpV0NkQdKReUSKW5tKve9uuWw1I6cjLN/nY75SdNQ6yCmqpyRyrcT7mTKD8M/ARt1cfP6H8/daFj1jlfk4jcLyKn9b+rrs4jIrfq+5wWkVtLtl8lIs+LSJ9e30z07Z8RkWEROaa/fmmzbfQqHQ7F0t0c6qiKhGmprbQ9BLQ8cO3O+9LhQAgokyswMbfoXoVrTKS03RBxr/xslnLDYh8Drgb6lVJvBa5AK2a5We4AHlRK7Qce1D+/At1T+jTwWuAa4NMlSuivgY+geVL7gZtLDv2iUuqw/tqGK1I6kwXk5lAHaErXboXr1tIvBh0NWgh1YdG+END5JW/OnR1pqediJ8M+WiTMoFzlktGXHEZEqpRSJ4GDW7juLWiLj6H/ffcq+7wduF8pNaWUmgbuB24WkQ6gXin1mD6p8+/WOH5bsqMhioj9noub1kNfDScmUiaSGVeHOjqX1nWx71kZSbmzYoFBe32UkNhf6DSRSrvWw90s5SqXIRGJA/8M3C8idwP9W7huu1Iqob8/D7Svsk8XWmWApTbo27r09yu3G9wuIs+JyNfWCrcBiMhtInJURI6Oj49v6ke4kYpwiLa6KluFI5t3d6gDtHCH3YPXbg91dDqwrkvC5Sm3mvzYOxa1sJgnuZBztfxshrKUi1LqV5RSSaXUZ4A/Ab7KOt6CiDwgIsdXed2y4twKMKuszF8De4HDQAL4f9faUSl1p1LqiFLqSGur++YhbAW705GNUIebLa/OeJTZbJ6ZTM62a7p9PfTlFG0bPRcPLIjVEbfXy10ute/ee7IZNuyvK6V+UuZ+N6z1nYiMikiHUiqhh7nGVtltGHhLyedutHVkhvX3pduH9WuOllzjb4D/VU5b/UZnPMrJ87O2Xc8L61AsTaRMZqjfYU9GWyKV5oqeuC3X2gzt9XoI1c6ONJWhqabS9koJG6GzIcaJhH0zLZYSP7aj52IB9wBG9tetwN2r7HMfcJOINOrhrZuA+/Rw2oyIvE7PEvst43hdURn8CtqKmdsOY/6CXXVGvWCNLo0v2NSRphcLTC/kXK1wKyMhWmqrbPVcvDC20BmPMpJK2yY/CQ8YZ5vBKeXyeeBGETkN3KB/RkSOiMhXAJRSU8CfAk/qr8/q2wB+F/gK0AecAX6ob/8veoryc8BbgT+w6fe4io6GKOlcgVTanhDQ8gqU7hWOUs/FDkZcnoZsoM11sTME5P7Kvx0NMTK5ItML9sjPcDKNiOZJ+glH0liUUpPA9atsPwp8uOTz14CvrbHfq2qdKaV+09yWehMjE2c4mSZebX2d0ZFUhsbqCmKV7g11tNVVERL7Bq8THplx3dEQo298zrbrJZIZXr+n2bbrbYblLLq0LauqJlJpWmurqIw4Zetbg79+TQBQsrSvTVZ6wgPWaCQcor0+alva7YhH4ugdca0KsB0hoJlMjtls3rWZYgZ2r+vi9jlimyVQLj6k0+aJlMPJNF2N7heOznjMthRtQ7G3N1TZcr3N0tkQY36xwEzG+omUXhlbsHs5guFk2lcFKw0C5eJDWmqrqAiLLbn6SimGp9OunRRXip0TKUeSaVrrqmxfQnijGB39sA3LNCx7c+7uSFtqqqgMh2wpdKqUIpHMuN7z3wyBcvEhoZCww6ZFj1LpHPOLBbq94rmkMhSL1oeAhpILnrgnRhvt6EjdPoHSYFl+rDfOUukc6VzB1ZmWmyVQLj7FrlpaxsJkXulIF/NFJuatXzfeK96cEc4ctmGBrKHpBSIhob3O3aFCsM/LNZS620OFmyFQLj6lOx6zxRo1lEtX3N512DeDoQCtXqmzWFSMJDN0N7r/njTXVBKtCNmyeunQdJqOeJRI2P3djjY+Z71xNuwh42yjuP+/HLApuhtjJFJpcoWipdcxFJgXBvQNBWj1+ML4XJbFQtET90RE6IrHbFEuw8k03R4wQkBLRz4/kyFvsfwse/7euC8bIVAuPqW7sZqiWq77ZRVD0wtUV4ZprHbfImEr6bLJczHWYPeKNdrdWG2Tl7vgCYUL2j0pFBWjs9aGUIem056Rn40SKBefYnRsgxbH0o2xBX29NldTWxWhsbpiqfO3iiVr1CNx9O7GmOX3JJsvMDqT9ZDC1Q2RKaufFS3xwwvys1EC5eJTDDfbeis97ZkOA7T7Ysc9AW+ECkFr5/RCjnkL1403xi+8Ev4x2jloi/x4455slEC5+JQdDdqiR1Z3pF6ZQGmgjS9Y77k011RSXenORcJWYnRuVobGvBYq7IxrFaOtf1a8kbK+GQLl4lMqIyF21EctFY7ZTI5UOueJTDGD7kYti87KcideVLhgbaKD17KiqiJh2uuilhpnqXSOmUzeM/dkowTKxcdYHQIyLF0vCUd3o1bxdnJ+0bJreM0a3bmU6GCdITI0nSYcEnZ4qPKv1WNRwz7OFINAufia7saYLdaol6x0q8eivFQOx6ClVit3MmRxWGxHvTfmuBh0N8YYnApChZvFO//pgA1j9VwXL3ouXRZb6RNzi2TzRU9Zo6GQ0NVo7VwXryV+AOxsqrZ0rouf57iAQ8pFRJpE5H4ROa3/bVxjv1v1fU6LyK0l2z8nIoMiMrdi/yoR+Y6I9InI4yLSa/FPcTVWz3UZmk5rqxnWuL+ch8FyuRNrOlJDaXnJcwEsn0g5nPReVlR3Y4xCUVlWet/Pc1zAOc/lDuBBpdR+4EH98ysQkSbg08BrgWuAT5cooX/Rt63kQ8C0Umof8EXgCxa03TNYPdfFCP+EQt7J0a+PVtAQq7CsI13y5pq8pVysDKEu5oucn8l4znNZTke2Rn78PMcFnFMutwB36e/vAt69yj5vB+5XSk0ppaaB+4GbAZRSjymlEuuc93vA9eLX/1wZWD2+MJT01tiCgZUDtcu11rx1X7riMSbmsmRyBdPPnUilUcpb4VOAnVbLj4/nuIBzyqW9RDmcB9pX2acLGCz5PKRvuxBLxyil8kAKcPeaqhZi9VyXgcl5djZ5TzisDAENT6dpiFVQF/VWqMPwtKy4L16bVGpgtfx4Latwo1g2y0tEHgB2rPLVfyj9oJRSImL9AhsrEJHbgNsAenp67L68LVg512Umk2N6IceuZu8pl+7Gah7pm0ApZXpIYmDKmx3GzpIQ0L62WlPPbTx/Oz1mpS/JjwUlYIw5Ll67JxvBMuWilLphre9EZFREOpRSCRHpAMZW2W0YeEvJ527gx+tcdhjYCQyJSARoACbXaN+dwJ0AR44csV252YVVc10GJjWB2+VBz2VnU4yFxQITc4u0mry2yMDUAoc66k09px306EZC/8Q8HDT33INT+hwXDy6IZZX8eG1S6WZwKix2D2Bkf90K3L3KPvcBN4lIoz6Qf5O+rdzzvgd4SFk5FdsDdDfFGLTA8hrQz9njQc/F8LYGpuZNPW++UGRwasGT96S1torqyjD9Fjwr/VMLdMVjVHhojotBd5M143NGkoDXQoUbwan/9ueBG0XkNHCD/hkROSIiXwFQSk0Bfwo8qb8+q29DRP6LiAwB1SIyJCKf0c/7VaBZRPqAj7NKFtp2o7e5hkQqY/pAbb/uufR40HPZ1VwDLP8Gs0ikMuSLil4PKhcRoaepeskjNZP+yXlPhk9B81wSMxkW8+bOdemf1AybXU01pp7XTThSWU8pNQlcv8r2o8CHSz5/DfjaKvt9AvjEKtszwHtNbazHMYR6cGqB/e11pp13YGqepppKzw1cgxaKCAmcM7kjXVa43uwwdjVXc2bcXG8O4NzEPO863Gn6ee2gp6kapbRxoz2t5o1FnZtcoLG6ggafznGBYIa+7+nVrXQrOlIvei2gFSXsaIgtWY9mcc6wRj1qpe9qrmFgaoFi0bxIcnJhkZlMfuk59BqGF2q2l6t5c968J+USKBefs2tJOMztSPsnFzzbiQL0tlSb3mEMTC0sZRh5kZ6m6qUJj2ZhGDVe7Uh7W7R2vzxhsiEyseDJ8OlGCJSLz4lXV9IQq1iyqs1gMV8kkUp7MlPMoKepxgKFO09PU7WnKhaU0mvBWFS/x7255ppKaqsipj4r2XyBkVTaswq3XALlsg3obTbXSh9Opikq6PGwcPQ2VzO9oK1HYxb9kwueVrhWZNF5OfEDtESH3pZqXjZRfgantIoFvS3evCflEiiXbcCu5hpTPRevW6OwHKYxKztKKcWAR9OQDToaokRCYur4XP/kAh0NUaIVYdPOaTe9zeZ6ucvy413jrBwC5bIN6G2uZng6bVo6pTHHxQ9WullKd3wuy8JiwbMD1wCRcIjuxpip6chGqNDL9DbXMDRt3tIVhvL28rNSDoFy2Qbsaq6hqMxbw6R/coFoRcj02e12shwCMueeGB2ylz0X0J6VfhPDYucmFzzfifa21FAoKtNm6vdPzlMXjfi21L5BoFy2AUZs16xxFyMN2csFp6srI7TVVXHOpCygcx4uh1PKLn18zozCFvPZPBNzWXZ5fGyh12Qv11C4XpafcgiUyzZg19JcF3OEY2Bq3rMTBUvZ1VxtWrmTgcl5QuL9VQV7mqqZzeSZXth6okP/ksL19rNipCObZYh4uWLBRgiUyzZgOZ1y6x1poajon1xgt8etUdBDQCYp3P6pBTrjMSoj3hap5XTkrd8XI+vM6x2pmfKTKxQZmk57PlRYDt6WhICyEBF2NVeb4rmMJNNk80X2mlgKwyl2NVUzOpNlYTG/5XO9PDHviw7DzEmDyxMova1cltKRTbgnw9NpCkXl+XtSDoFy2Sb0NteY4tafGZ8DYK/Ja344we5WI9yxNYtUKcWZsTnT10Fxgl3N1URCsvR/3govj8/TUuvN+nMrMSsd2TDwDCXuZwLlsk3obalm0IR0ZKOw4R4fCIfhffVtsSMdnckyv1hgb6v370lFOERPczVnxrbekfaNz/nCwwVNuQyakI58VpcfP3i56xEol23CvrZafbxka53GmfE54tUVNNVUmtQy59jdUkNIoG9sa8rFON4vHem+1totK1ylFH0+8eZgOR15q2sj9Y3P0RCroKXW+/KzHoFy2Sbsb9PK7Z/eYkd6ZkyzRv2QRhmtCLOzqXrLISDjeL90pHvbaumfnN+SlT4xt0gqnfPNPTF+hxmGyP42f8jPegTKZZuwRw/ZbFU4zk7M+yIkZrCvtZYzW1W443PUVUU8Pam0lL2tteQKW7PSjefMb8plq8aZn7y59XBEuYhIk4jcLyKn9b+Na+x3q77PaRG5tWT750RkUETmVuz/QREZF5Fj+uvDrz7r9qS6MkJ3Y2xLwpFK5xifzfpiMN9gX1stZyfmKWxhDZO+sTn2+MgaNcaOtrJwmBFW80uosLYqQlc8xunR2U2fY3Iuy9T8YqBcLOYO4EGl1H7gQVZZjlhEmoBPA68FrgE+XaKE/kXfthrfUUod1l9fMb/p3mVfW+2WPJezPuswQPsti/nilqz0M+Nz7PPTPTEhBHRmbI6ayjAdDd5c22Y19rXVbsk485s3tx5OKZdbgLv093cB715ln7cD9yulppRS08D9wM0ASqnHlFIJOxrqJ/a11nJmfG7TVvpLutXmJ+EwOtLNjrvMZnKMzmTZ2+afUGF9tIK2uqqtKZfxOfb6yJsD2K8bZ5uVH8ObM3O5cTfjlHJpL1EO54H2VfbpAgZLPg/p29bj10TkORH5nojsXGsnEblNRI6KyNHx8fGyG+5l9rdrVvpmC1iePD9LrCLs+fpZpWw1lm4oXCNhwi8caK9b+m2boW/MX94caPckuwX56Rubo7oyTKePvLkLYZlyEZEHROT4Kq9bSvdTWoU8sxbt/hegVyl1GZqnc9daOyql7lRKHVFKHWltbTXp8u5mn94BvjS6uY70ZGKWAzvqPLvS4mo0xCroaIhyMjGzqeNPJLQO+OIOfymXi3ZoyiW/iYyx5MIiiVSGAzv8dU/2teuGyCblp89HmZblYJlyUUrdoJS6dJXX3cCoiHQA6H/HVjnFMFDqeXTr2y50zUmlVFb/+BXgqq3/Ev9wUBf2zXSkSilOnp/hYp91GAAXd9QvKYmNcvL8DHVRbbDXT1zcUU82X9xUySDjXh7qqDe7WY5ieLkvjW38WVFK8eLIDBf5UH7Wwqmw2D2Akf11K3D3KvvcB9wkIo36QP5N+rY1MRSWzruAEya01TfUVkXoba7mxU0ol/HZLNMLuSUF5Scu7qjjzPgc2Xxhw8eeSMxy8Y5631mjF+me2GaUrvF8Xewz5VIfraArHtvUPRmfzTI5v8ihTn/dkwvhlHL5PHCjiJwGbtA/IyJHROQrAEqpKeBPgSf112f1bYjIfxGRIaBaRIZE5DP6eX9PRF4QkWeB3wM+aONv8gSHOus3pVxOntcE6qId/hOOizvqyRfVhsMdxaLi1PnZpY7YT+xrqyUSEk6e3/izciIxQ0ttlW/m/ZRySWc9LwynNnzcC7rM+c2buxARJy6qlJoErl9l+1HgwyWfvwZ8bZX9PgF8YpXtnwQ+aWpjfcahjnruff48s5nchgoKGp2MH916w8I+kZjh0q6Gso8bmk4zl837zkIHqIqE2dtay8lNWOknEjO+G4MyuKSzgftPjDKfzVNTVX73+eKI7s0FnkuAXzHccsMTKZeTiVna6qpo9EFNsZX0NtcQrQhtONxxwscKF7TQ2IkNerm5QpHTo3O+tdAv6axHKTZ8X15MzNDTVE29DypEl0ugXLYZhzo0y9ywpMrl2aEkl3WXb9V7iXBIOLijfuMdxsgMIlqKqh+5uKOekVSG6fnFso85Oz7PYqHo27EFw7M9vsHQ2ImRGd8q3LUIlMs2o72+iuaaSl4YKV84ZjI5zozPc3l33LqGOcwlnfUcH0lR3MAEuWODSQ601W0oPOIljP/3saFk2cc8r3e6fu1Il+WnfENkPpvn5cl53yrctQiUyzZDRLi0q4FnB8tXLs/p+x7uiVvUKue5Ymec2Uy+7Jn6SimODSa5wsf35LLuBkICzwwkyz7m6YFp6qIRX5UIKkVEONRZz/ENKJfnhlIoBZd2BcolwOdctauRl8ZmSaVzZe3/rG65XtYVt65RDnPlLq1s3dMD02Xt//LEPKl0ztfKpaYqwoH2Oo4NJss+5un+aQ7vjPtqou1KLu+O89LoLPPZ8pbHNp6pK3tWrc/rWwLlsg25alcjSsEzZXakzwwk2dNSQ0O1fwcj97TUEK+u4On+ZFn7G9b84Z3+7jCu6IlzbGC6rHDhXDbPS6Ozvu9Ej/Q2Uiiqsj26o+em2NdWS7zaf8kwFyJQLtuQwzvjhESzMtfDCP8c3hm3vmEOIiJcsTNetudybDBJbVXEV0U8V+OKnY3MZLQxg/V4djBJUS17gX7lql2NhASePDe17r7FouLpgSRHfH5PViNQLtuQmqoIF3fU81QZHWn/5AITc1lfh38Mruxp5PTYXFnhwqcHprl8ZwNhH4d/YHmcrRxDxNjH74ZIXbSCi3bUc7R/feVyZlx7nq4KlEvAduGqXY08M5BctzDhz/omALh2X4sdzXIUowN4ap1OY2p+kRcTM1zd22RHsxxlX2stzTWV/PzM5Lr7Ptk/zf62Whpi/g2fGlyzu4mn+5PrLgX9lK5wA+USsG147e5mFhYL6w7WPnJ6nK54jN0+Wtp4La7c1UisIsxPTl14CYZH+iZQCt50wP/VtEMh4Y37W/jZ6fELjrukFws8dnaS6/b7/56ANu6SzhXWTUl+pG+C1rqqbSE/KwmUyzbljftbiISEB0+uVpBaI18o8vMzk7xxX4vvCjOuRrQizBv2NvPwqXG0lSBW56cvjdMQq/D1vJ9S3rS/lYm5xQvWpHvs7CSL+SJvObg9lMvr9zQTEnj4AvKTKxT5yUvjvO1g27aQn5UEymWb0hCr4OreJh46sbZwPD+cYjaT59r9/g+JGbzlYCsDUwu8PLH6ALZSip++NM4b97X4frzF4LoD2v//p6fX9ugePjVGrCLMNbv9HyoEaK6t4siuJv73i6Nr7nP03DSzmTxvu7jNxpa5h0C5bGOuv7iNU6Oza66s9/DJMUIC1+5ttrllzvGWg1pH8OM1QmMnErOMzWZ504Hto3Db6qJc3FG/5j1RSvHjU+Ncu6+ZaEXY5tY5x42H2jmRmGFwanX5efDEKJXhEG/cBuOVqxEol23MWy/SOtIHVrG+lFL8r+cSvG5PM821/iudvhY7m6rZ31bLj46fX/X7Hzw/QkiW79124aZD7Tx5borRmcyrvjuRmGVgamFJMW8Xbjykrc5+/xry88CJUV63t9m35YHWI1Au25g9LTVc3FHP954eetV3xwaTnJ2Y55cv73SgZc7y7iu6eOLcFAOTr7RIC0XF3cdGuHZfC21122MddIN3He5EKfjnZ169GOw/Pj1ERVj4V6/pWOVI/9LbUsNFO+q4+9ir78lT/dOcm1zgX71mhwMtcweBctnGiAjvv3onx4dnXjVb/+9+0U9tVWRbKpdfuaKLcEj4+8fOvWL7gydGGZpO876rd65+oI/Z21rL1b2N/P1j/RRKssbmsnn+4eggNx5q9+VyDOvx/qt38uxQimdXZF3+z8f6qakM887Ltp/8GDiiXESkSUTuF5HT+t9Vk8BF5FZ9n9Micqu+rVpEfiAiJ/VVJz9fsn+ViHxHRPpE5HER6bXpJ3mWX7uqm3h1BV984PRShlTf2Bz3PDvCe490U7sNXfrOeIx3XtbBNx8fYEwPAxWLii89dJqueIybL9me1uiH3riboek0/1ji6d7183PMZPJ85Lo9DrbMOX71qm4aYhV88YGXlrYZ8vMbr9u1bUNi4JzncgfwoFJqP/Cg/vkViEgT8GngtcA1wKdLlNCfK6UuAq4ArhWRd+jbPwRMK6X2AV8EvmDtz/A+tVURbn/rPn760jjfemKQhcU8//57zxKrCPPRt+5zunmO8fs3HCBXVHziH58jVyjy5Yf7OD48wyduPkgkvD0d/rdfsoMre+L82b0nODcxz/HhFP/1odPcdKidK3xeT2wt6qMVfPSte/nxqXG++fgA89k8f/gPz1IXreC2N21PhWsgF8rnt+yiIqeAtyilEiLSAfxYKXVwxT4f0Pf5Hf3z/9D3+9aK/f4KOK6U+hsRuQ/4jFLqFyISAc4DrWqdH3nkyBF19OhR836gxygUFR/8+hP87PQEsYowmXyBL//6lfzSNouhr+R/PtbPH//zcWIVYdK5Arcc7uQv33d4W85ZMHh5Yp53f/lRFhbzFBXsqI/yT7/7Btrrt9cYVCkr5WexUOTLv34FN1/qf/kRkaeUUkdW/c4h5ZJUSsX194LmbcRX7PNHQFQp9Z/0z38CpJVSf16yTxx4GrhBKXVWRI4DNyulhvTvzwCvVUpNrNKG24DbAHp6eq7q7+83/Xd6iUyuwF0/P8fLE/P8yhVdvHbP9kk/vhAPnRzlR8fPc2lXA79+Tc+29VpKGZxa4KuPvExlJMSH3rh7WysWg2y+wNcfPce5bSY/F1IulgUEReQBYLXg9H8o/aCUUiKyYQ2neybfAr6klDq70eOVUncCd4LmuWz0eL8RrQjzO2/e63QzXMfbLmrnbRe1O90MV7GzqZrPvOsSp5vhKqoiYf5tID+vwDLlopS6Ya3vRGRURDpKwmKrTRMfBt5S8rkb+HHJ5zuB00qpv1xxzE5gSFc+DcD6FfcCAgICAkzFKR//HuBW/f2twN2r7HMfcJOINOoD+Tfp2xCR/4SmOH7/Aud9D/DQeuMtAQEBAQHm45Ry+Txwo4icBm7QPyMiR0TkKwBKqSngT4En9ddnlVJTItKNFlo7BDwtIsdE5MP6eb8KNItIH/BxVslCCwgICAiwHkcG9N3Gds8WCwgICNgMFxrQD1JfAgICAgJMJ1AuAQEBAQGmEyiXgICAgADTCZRLQEBAQIDpBAP6gIiMA5udot8CvKoCgM8JfvP2IPjN24Ot/OZdSqlV17YOlMsWEZGja2VL+JXgN28Pgt+8PbDqNwdhsYCAgIAA0wmUS0BAQECA6QTKZevc6XQDHCD4zduD4DdvDyz5zcGYS0BAQECA6QSeS0BAQECA6QTKJSAgICDAdALlsgVE5GYROSUifSLi+wrMIrJTRB4WkRdF5AUR+ZjTbbILEQmLyDMi8r+cbosdiEhcRL4nIidF5ISIvN7pNlmNiPyB/lwfF5FviYjvltgUka+JyJi+aq+xrUlE7heR0/rfRjOuFSiXTSIiYeDLwDvQyv9/QEQOOdsqy8kDf6iUOgS8DvjoNvjNBh8DTjjdCBv5K+BHSqmLgMvx+W8XkS7g94AjSqlLgTDwfmdbZQl/C9y8YtsdwINKqf3Ag5i0VEmgXDbPNUCfUuqsUmoR+DZwi8NtshSlVEIp9bT+fhatw+lytlXWo68h9K+ArzjdFjsQkQbgTWjrI6GUWlRKJR1tlD1EgJi+im01MOJwe0xHKfVTYGrF5luAu/T3dwHvNuNagXLZPF3AYMnnIbZBR2sgIr3AFcDjDjfFDv4S+ARQdLgddrEbGAe+rocCvyIiNU43ykqUUsPAnwMDQAJIKaX+t7Otso12pVRCf38eaDfjpIFyCdgwIlIL/CPw+0qpGafbYyUi8k5gTCn1lNNtsZEIcCXw10qpK4B5fL6qqz7OcAuaYu0EakTk3zjbKvvRl4U3ZX5KoFw2zzCws+Rzt77N14hIBZpi+YZS6p+cbo8NXAu8S0TOoYU+3yYi/9PZJlnOEDCklDK80u+hKRs/cwPwslJqXCmVA/4JeIPDbbKLURHpAND/jplx0kC5bJ4ngf0isltEKtEG/+5xuE2WIiKCFoc/oZT6C6fbYwdKqU8qpbqVUr1o/+OHlFK+tmiVUueBQRE5qG+6HnjRwSbZwQDwOhGp1p/z6/F5EkMJ9wC36u9vBe4246QRM06yHVFK5UXkduA+tMySrymlXnC4WVZzLfCbwPMickzf9n8rpe51rkkBFvHvgG/ohtNZ4Lcdbo+lKKUeF5HvAU+jZUU+gw9LwYjIt4C3AC0iMgR8Gvg88F0R+RDa0iP/2pRrBeVfAgICAgLMJgiLBQQEBASYTqBcAgICAgJMJ1AuAQEBAQGmEyiXgICAgADTCZRLQEBAQIDpBMolIMAB9KrDv7ti2w/1OmYBAZ4nUC4BAc4QB5aUi4jEgGal1JBjLQoIMJFAuQQEOMPngb0ickxE/h+0iW0/BhCRcyLyZ/p3R0XkShG5T0TOiMi/1ffpEJGf6vscF5HrHPslAQGrEMzQDwhwhjuAS5VShwFE5EvAP5d8P6CUOiwiX0Rbg+NaIAocB/478OvAfUqpz+lrC1Xb1/SAgPUJlEtAgDu4Fvijks9GnbrngVp9/ZxZEcmKSByttt3X9EKi/6yUOmZnYwMC1iMIiwUEOIyI7AEG9UXnDLL632LJe+NzRF/06U1olbj/VkR+y5bGBgSUSaBcAgKcYRao09+/A/jRRg4WkV3AqFLqb9BWyPR7SfwAjxGExQICHEApNSkij4rIcbSVDz+ywVO8Bfj3IpID5oDAcwlwFUFV5IAABxGRKuBRpdQRp9sSEGAmgXIJCAgICDCdYMwlICAgIMB0AuUSEBAQEGA6gXIJCAgICDCdQLkEBAQEBJhOoFwCAgICAkwnUC4BAQEBAabz/wMybEX5vHKYRQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "monotone.plot(0, 10, xlabel=\"t/ms\")   #Plot its waveform"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The power of the audio $P=\\frac{\\displaystyle\\sum_{n=0}^{N_{max}-1}x^2[n]}{N_{max}}$ determines the **loudness**. When we play an audio, its power will be displayed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00019999999999999996"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pyAudioKits.analyse as aly\n",
    "\n",
    "aly.power(monotone)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The power can also be expressed in the form of gain, $gain (dB) = 10log_{10} power$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-36.98970004336019"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aly.power(monotone, dB = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The energy $E=\\displaystyle\\sum_{n=0}^{N_{max}-1}x^2[n]$ is also a characteristic of audio. In the case of an audio signal with infinite time, the energy is defined as $E=\\displaystyle\\lim_{N_{max}\\rightarrow ∞}\\sum_{n=-N_{max}}^{N_{max}}x^2[n]$, while the power is defined as $P=\\displaystyle\\lim_{N_{max }\\rightarrow ∞}\\sum_{n=-N_{max}}^{N_{max}}\\frac{x^2[n]}{2N_{max}}$. In this case, energy is defined only for audio signals of mean square convergence, and the power of such signals is 0. Such signals are called finite-energy signals and often imply a signal that has a value only at finite time, or a signal that decays with time. A signal with infinite energy but limited power is called a finite power signal. Since we truncate the audio signal by windowing, all signals are time-finite, have finite energy and power and are scaled by $N_{max}$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.819999999999999"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aly.energy(monotone)    #Calculated energy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the energy may be a large value when $N_{max}$ is large, it can also be calculated in the form of gain, which is call logarithmic energy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.454685851318196"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aly.energy(monotone, dB=True)    #Calculating logarithmic energy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The power of a monotone is related to the **amplitude** of its corresponding sine wave."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The power of the audio:  0.0007999999999999998\n"
     ]
    }
   ],
   "source": [
    "monotone=monotone*2\t#Turn the amplitude into twice the original\n",
    "monotone.sound()\t#Try playing it"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The power becomes four times the original and the audio sounds louder.\n",
    "\n",
    "The change in amplitude can also be written in the form of gain. $ gain (dB) = 20log_{10}\\frac{new ~amplitude}{original~amplitude} = 10log_{10}\\frac{new~power}{original~power}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The power of the audio:  0.008000000000000002\n",
      "In order to protect your hearing, the amplitude is limited. \n"
     ]
    }
   ],
   "source": [
    "monotone=monotone.amplify(5)    #增益5dB\n",
    "monotone.sound()\t#播放一下试试"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The power is changed to 10 times of the original. At the same time, the hearing protection mechanism of the sound function is triggered."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we create a sine wave with higher frequency."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The power of the audio:  0.0002\n"
     ]
    }
   ],
   "source": [
    "monotone2=ak.create_Single_Freq_Audio(0.02,880,44100,1)\t#Generate a monotone with a length of 1s, an amplitude of 0.02, a frequency of 880Hz, and a sampling rate of 44100\n",
    "monotone2.sound()\t#Try playing it"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Frequency determines **pitch**. The $f=440Hz$ is called the central A. Doubling up in frequency is called an **octave**.\n",
    "\n",
    "In twelve mean meters, each **half tone** is doubled in frequency by $2^{1/12}$. The distance between any two tones is called the interval, and the unit of interval is **degree**, the interval between the same single tones is 1 degree, and after that it increases by 1 degree for each difference in pitch."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/harmonialeo/Documents/source/pyAudioKits/pyAudioKits/audio/audio.py:100: FutureWarning: Pass sr=44100 as keyword args. From version 0.10 passing these as positional arguments will result in an error\n",
      "  return Audio(librosa.effects.pitch_shift(self.samples, self.sr, n_steps=halfSteps),self.sr)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The power of the audio:  0.0001967911023878219\n"
     ]
    }
   ],
   "source": [
    "monotone2=monotone2.pitch_shift(-12)\t#Down-tune 12 semitones\n",
    "monotone2.sound()\t#Try playing it"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The original frequency of monotone2 is 880Hz, after 12 semitones of down-tuning, the pitch is the same as monotone whose frequency is 440Hz."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Frequency can be studied using **autocorrelation function**. The autocorrelation function $\\rho[k]=\\displaystyle\\sum_{m=-∞}^∞x[m]x[m+k]$ represents the structural similarity of a waveform before and after an offset of $k$ samples.\n",
    "\n",
    "Since we truncate the audio signal, the autocorrelation function is computed as $\\rho[k]=\\displaystyle\\sum_{m=-∞}^∞x'[m]x'[m+k],k\\in\\{-N_{max}+1, -N_{max}+2, ... , N_{max}-2, N_{max}-1\\}$, where $x'[n]=\\begin{cases}x[n],&0≤n<N_{max}\\\\0,&Others\\end{cases}$. When $|k|<<N_{max}$, the effect is almost negligible. The obtained $\\rho[k]$ can be represented by a vector of length $2N_{max}-1$. When $N_{max}$ is extremely large, a small part of $\\rho[k]$ is usually intercepted."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aly.autocorr(monotone).plot(-220,221,xlabel=\"k\")    #Compute the autocorrelation function of monotone and intercept the part of k taking [-220,221)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aly.autocorr(monotone).plot(-5,5,xlabel=\"t/ms\")    #Calculate the autocorrelation function of monotone and intercept the part of [-5ms,5ms)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It can be seen that the autocorrelation function has periodicity and is symmetric about $k=0$. Its period is around $k=100$. Since the sampling rate is $44100Hz$, 100 samples represent a time duration of about $2.27ms$. The frequency of monotone is $440Hz$, and its period is exactly about $2.27ms$. So we can determine the period of the monotone by the time interval of the local maxima in the autocorrelation function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fundamental waves, harmonics and Fourier series\n",
    "\n",
    "Next, let's explore the complex musical tones. First, 13 440Hz monotones are generated. On top of this, when generate the nth 440Hz monotone, generate another 1s monotone with frequency $440-2^{(n-1)/12}Hz$, which is linearly summed with the original monotone for **chords**, thus simulating all **intervals** from minor second to pure octave."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The power of the audio:  0.0002241272982532446\n"
     ]
    }
   ],
   "source": [
    "x = ak.create_Single_Freq_Audio(0.02,440,44100,1) + ak.create_Single_Freq_Audio(0.02,440,44100,1)\n",
    "for i in range(12):\n",
    "    x = ak.concatenate([x,ak.create_Single_Freq_Audio(0,440,44100,1)]) #Add a 1 second gap after each chord\n",
    "    x = ak.concatenate([x,ak.create_Single_Freq_Audio(0.02,440,44100,1) + ak.create_Single_Freq_Audio(0.02,440*2**((i+1)/12),44100,1)])\n",
    "x.sound()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The generated 26s audio has 13 chords with different intervals, some of which sound harmonious and some of which sound dissonant.\n",
    "\n",
    "1. minor diatonic intervals (one semitone apart) and major seventh intervals (five whole tones and one semitone apart) are highly discordant intervals\n",
    "2. major intervals (one whole tone difference), minor intervals (five whole tones difference), and triplets (three whole tones) are discordant intervals\n",
    "3. minor third interval (difference of one whole tone and one semitone), major third interval (difference of two whole tones), minor sixth interval (difference of four whole tones), major sixth interval (difference of four whole tones and one semitone) are not fully harmonized intervals\n",
    "4. pure fourth intervals (two whole tones and one semitone difference), pure fifth intervals (three whole tones and one semitone difference) are fully consonant intervals\n",
    "5. pure octave (six whole tones apart) is a very complete concord interval"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x.plot(4,4.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It can be seen that the waveform of such a chord is far from being called a sine wave, but this strange waveform is created by superimposing two sine waves of different frequencies. In fact, according to **Fourier series**, any waveform of a periodic signal can be expanded into the form of a superposition of sine waves of different phases, frequencies and amplitudes.\n",
    "\n",
    "A continuous time periodic signal, if its period is $T$, has **fundamental frequency**$\\omega_0=\\frac{2\\pi}{T}$. And any periodic signal can be represented as the sum of **fundamental wave component** and **k+1th (k=1,2,...) harmonic components**, where the frequency of the k+1th harmonic component is k+1 times the fundamental frequency $\\omega_0$. The weights of each component are called **Fourier coefficients** and are denoted by $a_k$ as follows: \n",
    "\n",
    "$x(t)=\\displaystyle\\sum_{k=-∞}^∞a_ke^{jk\\omega_0t}=\\displaystyle\\sum_{k=-∞}^∞a_ke^{jk\\frac{2\\pi}{T}t}$\n",
    "\n",
    "$a_k=\\displaystyle\\frac{1}{T}\\int_Tx(t)e^{-jk\\omega_0t}dt=\\frac{1}{T}\\int_Tx(t)e^{-jk\\frac{2\\pi}{T}t}dt$\n",
    "\n",
    "The Fourier coefficients determine the amplitude of each component.\n",
    "\n",
    "The Fourier series can also be written in the form of a trigonometric function: $x(t)=c_0+\\displaystyle\\sum_{k=1}^∞[a_kcos(\\frac{2\\pi k}{T} t)+b_k sin(\\frac{2\\pi k}{T} t)]$, where $c_0=\\frac{1}{T}\\displaystyle\\int_{T}x(t)dt$, $a_k=\\frac{2}{T}\\displaystyle\\int_Tx(t)cos(\\frac{2\\pi k}{T}t)dt$, $b_k=\\frac{2}{T}\\displaystyle\\int_Tx(t )sin(\\frac{2\\pi k}{T}t)dt$.\n",
    "\n",
    "The waveforms of musical tones from actual instruments in the real world are all quite complex. However, musical sound can basically be described by three elements, which are **pitch**, **loudness** and **timbre**. The loudness of the sound is determined by the power, as mentioned before. The pitch of the sound is determined by the **fundamental wave** with the largest amplitude, whose frequency is **fundamental frequency**. In addition to the fundamental wave, there are numerous **harmonics** or **overtones** whose frequency are integer multiples of the fundamental frequency. The amplitude of these **harmonics** or **overtones** determines the characteristics of the waveform and the **timbre** of the audio.\n",
    "\n",
    "Sine and cosine signals of 1, 5, 10, 20, and 50 frequencies are generated between 220-11000Hz to simulate harmonics, and the amplitudes are generated randomly and descending with the increasing of frequency."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The power of the audio:  0.0016094289253369737\n",
      "The power of the audio:  0.0006342329657102692\n",
      "The power of the audio:  0.0014485557278367813\n",
      "The power of the audio:  0.001302351598106276\n",
      "The power of the audio:  0.0016324227654416416\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import random\n",
    "\n",
    "random.seed(0)\n",
    "\n",
    "def generate_timbre(K):\n",
    "    return ak.synthesis([ak.create_Single_Freq_Audio(random.uniform(0.0,0.05)/i,220 * i,44100,1,np.pi/2)+ak.create_Single_Freq_Audio(random.uniform(0.0,0.05)/i,220 * i,44100,1) for i in range(1,K+1)])\n",
    "\n",
    "p = generate_timbre(1)\n",
    "p.sound()\n",
    "p = generate_timbre(5)\n",
    "p.sound()\n",
    "p = generate_timbre(10)\n",
    "p.sound()\n",
    "p = generate_timbre(20)\n",
    "p.sound()\n",
    "p = generate_timbre(50)\n",
    "p.sound()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have generated five electronic tones with different timbres."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aly.autocorr(p).plot(-440,441,xlabel=\"k\")    #Compute the autocorrelation function of p and intercept the part of k taking [-440,441)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYcAAAEGCAYAAACO8lkDAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8qNh9FAAAACXBIWXMAAAsTAAALEwEAmpwYAABK9klEQVR4nO29eXRr2Vno+dsabUuW59m+8+hbVbfq1k2lMpJQISQhpAIJdBIWCS806QChk/Xg8ZKmmwWPF8b3oGHBgw4JkEAgKRISKqEqU2VOaro13Ml3Hj1PsiVZsjXu/uOcY+vasi3Jks7ROfu3lpdtST7a3tpnf+P+PiGlRKFQKBSKfFxmD0ChUCgU1kMJB4VCoVBsQAkHhUKhUGxACQeFQqFQbEAJB4VCoVBswGP2ACpBZ2en3LNnj9nDUCgUirriueeem5NSdhV6zhbCYc+ePZw6dcrsYSgUCkVdIYS4tdlzyq2kUCgUig0o4aBQKBSKDSjhoFAoFIoNKOGgUCgUig0o4aBQKBSKDSjhoFAoFIoNKOGgUCgUig0o4aBQVJGvnJtifHHZ7GEoFCWjhEMZLMRTPHcrbPYwLEV0Jc3vP3aB0XDC7KFYhshymvf/03P83N8+ZfZQLMVnn73Nl05PmD0MSxFPZvjhtTmzh3EHSjiUwa98+nne9tdPshBPmT0Uy/CZZ27zse9e55FTo2YPxTKcHl0E4Oa8EpgGUkr+6+fP8mv/8gKZbM7s4ViG//NfXuBdf/s009EVs4eyihIOZfDsTc1qeOamsh4MZmNJAKYi1lncZjMZUe6k9Swm0qs/T+trRgFPXJwB4OxYxOSRrKGEww6wkpQ3mxn9Rh9dUFqywXyeZZnKKC0Z7lwfEyoWs0qzXytzd3M+bvJI1lDCoUSklBhdt2eV5rOKISjVnKyR73YMKxckcOf6UFbmGpmctqvMW2idKOFQIrFkhqz+Qc4tqY3QwLAc1Ca4Rv6NrtaKxvzS2pwsJNRaAVhJZ1lOZwGYt9A6UcKhRPK1wdmYWtwGs1FtUS8up1eFp9NZUMJhA/PKmtpA/jzkC0+zUcKhRJQ2uJFEKkMsmaE31ICUSiM0CMdT7O5oAqx105vJ/FKSRq+blkavEg46+fMwZ6E5UcKhRML6Tb6/K6CEg86cbkEd7m0GlEZoMB9PcbA7qP+s1gpoc9IR9NER8Kl1omMonEPtjcqtVM+EE2sb4WwsiZTKhWLMyepGqLRkQHMr7WoP4PO41JzozC0l6Qj6aQv4lIWpE9YVh8M9zZZaJ0o4lIih7RzsbiaZyRFPZU0ekfkYvvUDunBQGqEWZIynsnQEfXQGfMxZ6KY3k3A8RUfAR1uTz1IboZkY83Cwp5nldJZ4MmPyiDSUcCiRcDyF3+NioK0RQJ2SJk9g9hjCwTqmsVkYWnFbk4+OoF+5lXTml1K0BzS3krIcNMLxFG6XYG9nALCO5a2EQ4nkL26wVl6yWRg3+b5Ow7+u5sS4wdsDPjqDSksG7YxQWI85tOkxB+WW1YRDW5OPrqAfgDmLKBJKOJTIQkITDu26cFCWgyYMvG5Ba5NXZaHoGHPQHtAsB5W8AIlUllQ2R3uTj/aAl3RWsmQRF4qZGK62jqCucFpEkfCYPYB6Yz5+p3BQWrImINuafAgh6Aj41JywZk0ZVua8riULIUwemXkYArOtyYfLpc3DQjxNc4PXzGGZTljfUzp0y8EqGUvKciiRcDypLId1GIsbtM0wbBHNx0wM7a8joLlQUip5YS0OE9AsB1ApvqDfP0HruaqVcCiRhXia9oCPoN+D1y0s80GayUJCsxxAFw5qTlhIpHAJaGn0rgpOpwvNBb0ia3vAS3vArz/m7DkB/exHwEeD103A57aMW8lU4SCEaBVCfE4IcVEIcUEI8TIhRLsQ4utCiCv69zYzx5hPMpNlKZmhI6C5UNoDPmU5cKfl0BFUbiXQbnjDfbKmETpbS17Icyu1N1nLv24W6WyOyHJ6zfIO+iyT7We25fDnwFeklEeA48AF4MPAE1LKg8AT+u+WYC3IqGk9bU1qIwRNI2zT3QTteopizuH1lcJLKdryXG2gtOT8mIOxXpw+J8b/37G6VvyW2VNMEw5CiBbg1cAnAKSUKSnlIvAw8En9ZZ8E3mrG+Aqxlp5450boZLI5yWIitaoJtgf8ZHOS6Ep6m7+0N+FEnjUVMAKNzl4rhqst1Ogl6Pfgc7sIxx2+TuJrcRjAUmVFzLQc9gKzwN8LIV4QQnxcCBEAeqSUk/prpoCeQn8shHifEOKUEOLU7OxsTQa8loHi179b54M0i+hympy8c3GDdYJqZhGO5wlMPUXR6WtlIZGitcmH2yUQQtAW8FrGhWIW+SnPxnerrBMzhYMHOAH8tZTyPiDOOheS1E7IFPRPSCk/JqU8KaU82dXVVfXBgrU/SLMIJ+6ckzaVxQVo/78hFAI+t64lO31O0rQ1raWttjX5lOUQN9xKfv37Wtqz2ZgpHMaAMSnl0/rvn0MTFtNCiD4A/fuMSePbQP6pV+N7ZDlN2sGN0vODjMCqtuzkjTCXkywkUqtWlJG8oKyptaw20JIXlOWwcU9JZXKWOBxomnCQUk4Bo0KIw/pDDwEjwKPAe/TH3gP8uwnDK4jhM21tXIs5GI87lfWL2wg05jeSdxoRw9WWtxEqK1NPeQ6szUlbk281vdWpGAqnYVGtpj1bYK2YfUL614BPCyF8wHXgP6EJrEeEEL8I3AJ+1sTx3UF+eiKs3fyLiTTdzQ1mDs001gfUVhe3gwWmYSEY5RCMn61ww5vJQiLF8cHW1d+tFHw1i3A8RWuTF49b09NXS2jEU+zuCJg5NHOFg5TyReBkgaceqvFQiiK8tJaBAmvBVycv8HDiTs2n0evG53E5OuYQXudqA01o3ppPmDUk05FSshBP0xrIiznkuWW9brOz6s0hP3EB1pJdrHBg0pmfSJmE4+vMYhV8JbyUosHrosmn6RlCCNqbnK0Rrne1gRF8de6cLCUzpLK5VYUK1ubHyS7Ieb0cj4GVFE4lHEognBdkBOVCAWNO/Hc85vQuX+FCbqWAj6VkhmTGmfWV1h8g1X62zkZoFvnVBeBOt5LZKOFQAus/yFbdleJoy2HdnIB2SNDJgcb8Rj8GTj/rsBqHyVeuVGYb4Xj6DiWiyeehweuyRBaXEg5FktXTE/M3Qr/HTdDvcXSudiHh0Nrk7JpT80spAj43DV736mOrhwMt4Es2g4V1iQugBGauwJ4C2pkHZTnUEYuJFFKy4YNsC3gd7UKZX7rT1QaaRuhoV1s8eccmCGvuFKeulYKWg8PdstGVNNmcvMPVBtZJe1bCoUgWEhuDjKBthFaQ8mZRyHIwslCyDi2+F06kNwpMh/vXNwvSgzUyc8xgfnVO7mx2pIRDnbHWvGWjlHeqC2U5lWU5nV11Dxi0N3mRUjsM5kTC6zJQYG1TdKpbKRxP4fe4aPKtudq8bhehBo9jralCQXrQS2hYYJ0o4VAka4e97pTybRaR8mZg9CfIz9OGNb+yU+dlIZ7e4FZqbfTiEs6dE8PCXN8m1cllRfK7BeajLIc6I5zYxHJocm7a5kLc6Oy1Tjg0ObusyHw8ueGGd7mEo/t/FHI/grMt70KuNtAC9cvpLMsmt5VVwqFIDL9oIcshkcqyknZe/rphOXSsdys52HJIpDKspHMbLAcwNELzUxTNYH4L4eBUgblZHNMqnQOVcCiS+XiKoN+D3+O+43EnF9/bzGfq5JPj4QJZOQaaluzMOMxCfGNWGzjbciiU8gx5JTRMnhclHIpkM7O4zcEHeTY1i1fdSs7bCAvVVTLQ+ms703JYX3rGwIjZWaF/Qa0Jx5MbkjnAOskLSjgUSaHDKpBnOThQI5yPp/C6BaGGO+s3NvrcljnlWWsKlc4wcGp9pWQmy1IyU9By6Aj4SGVzxE32r5vB/LqiewZW6aaohEORzC9tLRyceJAnvKSVMF+fgQL6KU8LpOPVms1cbaDd9IsOPP+xlriwcU6cfNZhM29Ex+rJcRVzqAu2yrYACC85UEvexJoC6Az6mHOglrzaLbCARtge8CGl8+JTqynP65I5IG8jdNicgLGnbBSYQb8Hn9ulLId6QEpJeJOAWouev272B2kGmwlMgI6gn3kHCsyZ2Ap+j4tQ48ZWKe1BawQaa81W1tRa8NVZayWXk8wtJelq3jgnRltZs60pJRyKILKcJpXNFfwg3S5Be8DPnAM3wi2Fg0VOedaamViS7pB/E1ebM5MXNktcgPzKrM6K2S0kUqSzkp7Qxj0FrHEQTgmHIpiOaht/T6hwK9DOoI/ZmPOEw/zSxsNeBp3NfubjScdloUxHV+jZpGWsU89/bJXea7iVnKZczej7xWbthbXMNiUcLM90dAXYXDh0NfuZdZiWnM7miK5kCroKQNsI0llJdDlT45GZi2E5FKLdIlkotSYcT+ESmgt2PQG/hyaf23HK1dqeoiyHusaQ8pt9kJ1BP3MOW9zGwaVCedqgzQnAnMN8ybPR5KbaoFMzc+bjWlaby7XR1Qa6cuWw+2c7y0EJhzrBkPKbfZCdQR9zS85yoazVmtosIG2Ngzy1JJHKEEtmNrUcfB4XzQ0exwVfw5ukgRt0O1A4GP/vZmvFCm1llXAogpnoCs0NHhp97oLPdwb9JDM5lpLOcaEYi3vTmINuOTgpY2nGiE1tokSAHqh3mFtpJray6SYIhlvWOesENIUz1ODZUDrDwAolNJRwKILpaHLTeAPkuVAcpCVPRTRrqrdl84Aa4KizDqsW5hYbYXvAeVV8t7t/uoLOsxxmokm6t5gTK5TQUMKhCKZjK5vGG0DLzAFnZVxsF6Q3UhQdZTls40cGvQqpg5SIXE4yE1vZWjg0+4kspx1V2Xi7PaXDAv21TRcOQgi3EOIFIcSX9d/3CiGeFkJcFUJ8VgixubOyRsxEk1u6CjoNLdlB2s90NElrk3dTs9jjdtEecFaK73YZKGCNQGMtCev5/L3bCAdwlnI1s0XiAlgj7dl04QB8ELiQ9/sfAX8mpTwALAC/aMqodKTUNJ+urXymQect7qnoypY3PGhWhbFhOoHZWBKfx1UwZdOgPeB3VBXSYgSmIRycokhIKZndIuUZrFF8z1ThIIQYBH4C+Lj+uwB+FPic/pJPAm81ZXA6C4m0dpJxGynvEmtuBScwHd3aVQDQG/IzGXGOcJiOrtDdXPh0tEF3s59MTjqmnPl27keArqD2nFOEw2JCq7iwleUQavDicQlT3bJmWw7/L/CbQE7/vQNYlFIaaT9jwIAJ41qlmMXtcbvoavavBmmdwFRka58paMFqJ1kOM7Ek3QVKrOTTpwfwJyPLtRiS6UxFtM1ts8QFWAvgO0W5mo5tb025XIKuZr+pc2KacBBCvBmYkVI+V+bfv08IcUoIcWp2drbCo1tjuwNwBr0tjY7RkjPZHHNLyW3dSr2hRuaWUqbmateSoqwpfZN0iiIxHV1BiLWMvkJ06Ja3UxQJI+V5K8sBtLViphJhpuXwCuAtQoibwGfQ3El/DrQKIYySloPAeKE/llJ+TEp5Ukp5squrq2qDLMZyAOgLmftB1pK5pRQ5CT1baIMAvS26Rhh1hkZYnOXQCOAYRWI6ukJn0I/XvflW43G76G5uYGLRGXNSrMLZb7LCaZpwkFJ+REo5KKXcA7wD+KaU8ueAbwFv11/2HuDfTRoioB2AAwpWZM2nr7WByciKIwKNU/qcbGs56BuhEzTC5VSW2Epmy9x10NaR2yUcZTlstwmCcf84Q7naruKCQW9LA1Mm7ilmxxwK8V+B/yyEuIoWg/iEmYOZjiZpadw8ZdOgr6WBRCpLzAGnpI2NbfuAtOFft/9GOBMzbvitN0K3S9Dd7JxA/VR0e/cjQH+rc9yys7HklhUXDIw9Jbpizp5iCeEgpfy2lPLN+s/XpZQPSCkPSCl/Rkppqk9iZpvDKgaGluwEjdDQfLYKMuY/7wTLYc1VsP1G2NvSwFTUGVryTBFxGID+lgYmFpcdYXkbWW3b0Wty8oIlhIOV2e7ov8FaFor9N8Lp6ApetyjYCjOfUIOHRq/bMXMCW5fOMOhraXDEnKQyOebjqSLvn0aSmZwjUny12FRxcwLm7SlKOGzDTHSlqA/SMJ2nHOA3ndLnZLMSzAZCCF1Ltv9GWEzRPYPeUKOpvuRaMV1kbAqgv1V7zcSi/e+fouMwJme2KeGwBVpdmK1PMhr0OMi/PhVZ2dalZNAbanCGqy22gs/torVp89PRBmb7kmvFVJHuRzBfS64VWsWFrYvuGXQ3+3EJmDRJYCrhsAXhRIpMTtJThH/Q53HRGXTGQbiShEOLM4TDbFRrFr/V6WgDp5x1MP6/vmKEg0Msh+hyhlQmV1TMwUjxVW4lCzKzTe/o9TjBlyylZDKyQl+Rc9Lb0sBMbIVczuYulG16FuSz6i6wubttNautCOHQGfDjdQsmbO6WNU5HF2M5AKa6ZZVw2IJSP8g+k0801oLocobldLYkt1I6K23f4Ga7yr35rFkO9l4rk5EVAj43zX7Ptq91uQR9LY1M2vwg3FpsqnhFQlkOFmSmiIqS+TjBcijFjwxrVpfd01mno8VbDt3NDQhhf//6VHSZ3paGolxt4AzlaqrIigsGmsA0J8VXCYctmNal/Hanow16WxqJrWRs3S7UuHmL8SPnv87OG+FKWgsuF+NHBufEp0qJTYF2EM7uJTSM4HKx89LX0kDcpMO1SjhswUxshbYmL37P1icZDcxOPasFa+1BG4t6fa8D/OurhdSK1AbBIVZmZIXeUHHrBLQ5mY6ukLVxfGoyukJ7wLdtxQUDM5MXlHDYgmIPwBk4IQtlMqJV2SxWS+4MGrWE7OsuWCvBXMJasXmKbzYnmY4li7YwAfpaG8nkpK2bZk0uLpc2Jy3mZXEp4bAFWs+C0j9IO/tNpyLbV9nMx6glZNT1tyPGjdtf4k1v53Uyt5Qkm5NFZSoZ9Ju4EdaKychKyQITlOVgOSYWl1dPbhZDT8j+lsNUtLTFDdq82LmWkOEeMm7kYuhtaSS6kiFu0/jU6hmHkpQrbf7sHHfQ7p/i14nWWdCcmJ0SDpuwks4yH0+V9EE2eN20B3xM2ti/rvmRSxMOfTY/CDe5uExzg4dgESmbBnY/6zC5GpsqJSBtb8t7OZVlMZEuaU68bhddJiUvKOGwCcaH0V+CNggO2AgjyyUtbtAtBxvPyUSJrgKwf3zKiDGVslZaGr00+dy2tRwMoVeKNwI0i9SMw4FKOGyC8WGU4kcGe2ehxJMZoiuZkoVDf6uWjhdZtmfFzcnIckkWJtg/xXcqmsTndm1buTcfIYStYzGr1lQJGVygueaU5WAhjJOapfiRwaglZM/FbbhAStWSB1qbABhfsOe8TC6ulKwN9ti8iu9UZJnukH/byr3r6W9tZMKmAnM1NlWGlamEg4UwMiZK/SD7WhpZSKRZTmWrMSxTmSpT8xloMwKN9tsIy4lNQV58ysYbYan3DuiWtw3XCZR+AM6gv7WBWDJDbKW2lrcSDpswESntsIrBal8HGwYaywkywpqPddyGN/10mdYU2Pusw2RkpeiDkvn0tTQyu5QklclVYVTmUuoBOAOzukwq4bAJk5HS0lgN7HzWoVxrqjPgx+dx2VI4GMHTUhMXwL7xqVxOMhUp3dUGmiIhpT1rcZV6AM7ArPiUEg6bMLlYWj6ygZ2zUCYjy3QGS9d8XC7BQGujLWMOpdaayseuXfLm4ylS2Rz9ZVoOYM9Afbmutl6Tzk8p4bAJE4vLJWcqgb0X9/jiSlkaMqAJBxtaDmtBxvIsh3A8xUraXvGp1RPjZawV42/sGJ/ShEPpc9IT0qr41jqdVQmHAsRW0sSSmZIzlQAafW5am7y2tBw0gVmecOhvbbClcJhYXKa1yUujrzRrCtZ8yXZzoezEmlrtJW0zt2wilSGyXNoBOAOzqvgq4VCAyTIPwBn0huznS5ZSaj7TMvzIoKWzzsaSttOSy9UGwb5nHYw4zEAZ90+Tz0NLo9d2TX/W9pTy7h8z4lNKOBSgnEJq+fS12K+WUHQ5QzyVLeuGh7V0VvtthOW5H8G+8amJxWUavC5am7xl/b0dD8KVmwZuYEblBSUcClBOIbV8elvs17Rk9cT4DmIOYD9f8sQOrCnDcrCbu20yosWmiu0Atx47Nv0pN9PPoK+l9iU0TBMOQoghIcS3hBAjQojzQogP6o+3CyG+LoS4on9vq/XYRsMJPC5RdJ/X9ezuaCIcTxGt8aGVarKTICOsCQc7ZSwtxFNEVzLs6QiU9fdNPg/dzX5uzsUrPDJzmYiUH5sCe1oOt+YTuF1i1YIulYFWrcvkYqJ2vdjNtBwywK9LKYeBB4FfFUIMAx8GnpBSHgSe0H+vKTfm4uzqaMJTZM+C9ezr1DaLG7P2uelvzScAGCxzcWu9hGHMRlryjXnt8y1XOADs6wpw3WbC4dZ8gqH28oVDf6v9qgzcmI8z2NZYdB+U9ezr0tbYtRruKaYJBynlpJTyef3nGHABGAAeBj6pv+yTwFtrPbYbc/HVDb4cjA/y+txSpYZkOtdml2ht8tIRKL6QWj4+j4ue5gZbuZUMjX9vV/lrZW9nkOuz9lkni4kU4XiKfZ3Bsq9hx4OkN+fiO1QitPms5VqxRMxBCLEHuA94GuiRUk7qT00BPZv8zfuEEKeEEKdmZ2crNpZcTnJjLs7eHQiHofYmXMJelsPVmSX2dwXL9iMDDLU3clu3QOzAjbk4LgFDbU1lX2N/V4CFRJqFeO3cBdXE0Gz37UBgGi7IUZu4IKWUunAof50MtTXidYuaWpmmCwchRBD4PPAhKWU0/zkppQQKdhuXUn5MSnlSSnmyq6urYuOZiCyTzOTYswPh4Pe4GWpv4pqN3AXXZuPs38END3CgO8iVmRjax1r/XJ+NM9TehM9T/m1kKCF2cS0Zmq2h6ZbDgW7tb69MxyoyJrOZjSWJp7I72lM8bhe72pu4NmMhy0EI0SOE+IQQ4nH992EhxC9W4s2FEF40wfBpKeW/6Q9PCyH69Of7gJlKvFexXJnWJv9QT/OOrrO3M2AbyyGSSDO3lGT/Dm54gIPdzSwk0szbREu+NB2ryDoBzQqxA9dm43jdgqEyY1MAHUE/HQHf6r1Y71zW/4/DO1wr+7qClrMc/gH4KtCv/34Z+NBO31ho/olPABeklH+a99SjwHv0n98D/PtO36sULk5p2spOb/p9nUGuzy2RzdW/lnxV1wYNja5cDvZof3/ZBhphMpPlxlx8xzf8UHsTXrfgag01wmpyaSrK/q5g2ckcBgd7glyeqf91ApoSAXCod2drZX9XkFvzcTLZ2lSsLeYT7JRSPgLkAKSUGaASaQSvAH4e+FEhxIv615uAPwR+TAhxBXid/nvNuDQVpa+lgZbG8g7wGBzpa2YlnePWfP1rhIYpu1PLwRC4dtgIr8/Gyebkjm94r9vFge5mLkxGt39xHXBxKsaRHc4JaFbm1eklW7ggL0/F6Aj46AyWlxpvcKgnSDora2Y9FNMRPS6E6ED3/QshHgQiO31jKeX3gc2imw/t9Prlcml6icMVWNzDfSEALkzGduR/tQIjk1GafFocZSd0N/tpbvDYwnIw/oedWg6grZXvXqlcUoVZRBJpJiMrHNHX/k441BMklsysHqirZyrhfgQ41t8CwPmJSEWutx3FWA7/Gc3Vs18I8QPgU8CvVXVUJpHO5rg2s1SRG/5AdxCPSzAyuWM5ajojE1GO9DbjLrHl43qEEBzqaebSVP0Lh0tTMTwusaOsNoPh/hCzsSQzsfo+FXxxSrN+KmE5GJtfva+VXE5yZTpWEYVzf1cAv8fF+fHaWJnbCgf9LMKPAC8H/g/gmJTyTLUHZgY35uKksrmKfJANXjcHuoNcmKz/xT0yGWW4f+faIMA9gy2cHY+QrpHftFqMTGq+9Z1kKhnkW5n1jBGvO9K787VybKAFl4AXRhd3fC0zGV1IEE9lK6Lpe9wujvQ2c37CIsJBCPFu4F3A/cAJ4J36Y7bjxduLANwz2FqR6x3tCzFSow+yWtycj7OUzHCXbtLulPt2tbGSztW1RpjLSV64vci9Q60VuZ4hHM5P1LeVeW48QnvAR09oZ751gKDfw+HeEC/cXqjAyMzjRV24HR+qzP0z3N/CyGS0JrGYYtSel+R9vQr4HeAtVRyTaTx3a4HWJu+O8/kN7h5oYSq6Utengp+9GQbg5J7KlLg6sasVgOfr+Ka/MR8nspzmxO7WilyvpcnL3s4Az92s3zkBOHVrgft3t+3ooGQ+J3a18sLtxbrO+Hvh9iJNPndFXNWg7SmR5XRNUp+LcSv9Wt7XL6FZD/UdYd2EZ2+FObGrcov7pfvaAXj6xnxFrmcGz9xYoD3g23GmksFAayNdzX5e0K20euSZG5rAvH935WpCPrivg2duhOt2I5yNJbkxF+clFVIiQJvfpWSGK3Wc0vrszTD3DLbsOLXX4EF9T3nyevX3lHJGHAf2VnogZnNzLs712TivOthZsWse7Q3R0ujlh1frUzjkcpLvXZnlpXvbKyYwhRA8sKedH1ydI1enG+ETF6YZaG2smMAE7aaPJTOcHlus2DVryfevatlWD+ztqNg1X7JH2wi/d3muYtesJTPRFc5PRHnVwcpVcNjbGaCvpYEfXK3+nBQTc/iSEOJR/evLwCXgC1UfWY35xoVpAF53tGApp7JwuQSvOdzF10amSWbqr8Lk87cXmIklecNdvRW97uuP9TATS/LCaP25UeLJDN+/OsdDR7srJjABXnO4G5/HxaMvTlTsmrXk8bNT9IYauGegMr510A4IHusP8fi5ye1fbEG+eVEr7vCjR7ordk0hBK890s23Ls6ylMxU7LqFKMZy+B/A/9S//gB4tZSy5mW0q4mUkn89NcbdAy07zuVfz0/dN0BkOc23Lta0CkhF+Pzz4/g9roouboDXHtE2wi+8MF7R69aCR09PsJLO8fC9/du/uARaGr382NEeHj09UXeZXAvxFN++PMsb7urFtcN05/W86e4+nr+9WJeVaz/33Bh7OwMVSe3N520nBlhOZ3n8bHWFZjExh+/kff1ASjlW1RGZwHO3Frg0HePnXrqr4td+5YFOOoN+HjlVX9MWSaT54gvjvPXeAZobdnZafD2hBi9vvqePLzw/TqzOGiL9yzO3OdzTzIldle9B9dMnBgjHU3zl3FTFr11NHjk1SiqT450PVP7++ZmTg3jdgn986lbFr11NLk/HOHVrgXc+MFRRCxPgxK429nYGeOTUaEWvu55NhYMQIiaEiBb4igkh6js/cx0f/94Nmv0e3lJhbRC03OSfe+kuvnlxpq5KJHzqyZssp7P8/Mt2V+X6737ZHuKpbF0JzSevzXNmLMK7Xrqr4jc8aK6lfV0B/upbV+smHrOSzvKpJ2/xwN72ipwPWk93cwNvuruPz50aI5KoH0Xi739wA5/bxdtODFb82kIIfu6lu3j25kJVs/42FQ5SymYpZajAV7OUsjInoizAD6/O8ZXzU7z3lXtp8hVTTaR03vuKvQT9Hv7HVy/VRa2Yc+MR/uKbV3jjXb3cVUEfcj73DrXy4L52/vKbVwjXQZXWRCrD737pPL2hBv63lwxV5T3cLsEHXnuAi1Mx/uXZ21V5j0rzB49dYHxxmQ8+dLBq7/H+H9lPPJXhj796sWrvUUkuTcX411NjvOOBITp2WE9pM975wC7aAz5+90sjVSvEV3S2khCiWwixy/iqymhqzPXZJX75089zoDvIL716X9Xep6XJy4ded5AnLs7w8e/dqNr7VIKVdJYPfuYF2gM+fv+n7q7qe/32m48RT2X55X96zvJ+9v/ni+e5NB3jD952Nw1ed9Xe5+F7B3j1oS5+59HzqweorMq3L83wySdv8d5X7OUVByqX5beeo30h3vuKvXz66dtVd6XslNhKmvf/03O0BXz82o9WT2AG/B5+9y3HOD26yEcfu1CV9ygmW+kteoXUG8B3gJvA41UZTY0ZW1gm1Ojh73/hJQT91bEaDH7xlXt54129/NFXLlo6uPaZZ25zbTbOn7z9OG1ltgQtluH+EH/403fz9I0wn3nWujf9qZthPv/8GB947QFee7iywfn1uF2Cv3zXfbQ2+fj9/7hgWUszm5P87pdGONAd5DffcLjq7/fhNx7hwX3t/Pcvj1Q9S2cn/PFXLnE7nOCv3nWCrubqWA0GP3m8n//28DF+4eV7qnL9YiyH3wMeBC5LKfeiVUx9qiqjqTGvPtTFN3/9NRXPUCqEEILfe+tduFyCj3/fmtZDNif5ux/c5MSuVl59qHK52VvxU/cNcN+uVv6/71yz7AGwT3z/Bi2NXn75Nftr8n6hBi8feO0BnrkZtmxtocfOTnJjLs5vvP5QVS0pA4/bxYffeJToSobPPGNNl9tCPMUjp0b5mfsHeWBve03e890v28PuHfSm3opihENaSjkPuIQQLinlt4CTVRmNCXgrdHKxGDqDft52YoDPPzdmST/7185PcTuc4JdeVT0X23qEELzvVfsYW1jmO5etl+47vrjMV89P8a6X7qpaTKoQb7t/kKDfwz8+ac0snX986ha72pt4/XBlz8Bsxb1Drdy/u41/fvq2JS2qf37mNslMjve+0h5nhIvZGRf1Ps/fAz4thPhztFPSijJ4z8v3kMzkePRF6+X4f+bZUQZaG3n9sdrd8ACvG+6hq9nPp5+ynkb4xRfGyUl4VxXSNLci6Pfw0ycG+I8zk0SWrZWlc3UmxjM3wrzrpbsqfq5hO971wC6uz8V56nq4pu+7Hdmc5FNP3uRVBztr0muhFhQjHL4FtAAfBL4CXAN+spqDsjNHekMM94UsdwAsspzmh9fmePM9fTvu21AqXj3l71uXZiyXrvil0xPcv7utJq7H9Tx8bz+pbI7vXrZWI6BHX5zAJeDt91c+TXM7fuKePgI+N186Y62T5C+OLjAdTfIzJ6uTyWYGxQgHD/A14NtAM/BZ3c2kKJM33NXLmfEIiwnruJa+f2WOdFbW3GoweOhoNzkJP7xmnTo6c0tJLk7FeOhodYPQm3HvUBttTd7VMgxW4btX5rh3qHXHbS/LocHr5mX7O2pSW6gUvj4yg0cvl2MXijkh/btSymPArwJ9wHeEEN+o+shszMv3dyAlljKNn7+9gN/j4p7B6pxr2I57h1oJ+j18z0I3vVF99cF9lSsmVwpul+Dl+ztXx2EFIstpzowtVrSYXKm88kAnt+YTjIYTpo1hPU9dn+e+Xa2EKlxNwExKicbOAFPAPGCOKmUT7hlspdHrtlQp7xduL3DPYEtNA/T5eN0u7tvVutpwyQo8cyNMo9fN3VU6CFgMx4daGF9cZm4padoY8jkztkhOrlVMNYOT+ntb5RxIKpNjZCLKfVUoqWImxZxz+BUhxLeBJ4AO4JeklPdUe2B2xudxcaw/xLlxa3T+SmaynLPA4r5nsIXL0zFW0taoYDsyobVHNUtgwlpXwjMWKeV9Vl+zZgrMQz3N+Dyu1bGYzcWpKKlsrmKdAa1CMat+CPiQlPKYlPJ3pJQj1R6UE7hroIXzE1FL5PZfmIyRyuS4z+TFffdAC5mcXO1FbCZG7+xjFeqdXS53672UT49aYyM8OxZhd0cTLU3muU98HhdHe5s5O2aNOTm92gq01dRxVJpiYg4fkVK+WIOxOIq7BlpIpLI1afe3HWd1rfQes4WDriWftYCWPLqQYCmZWe3vbBYBv4cD3UHLNAE6Ox4x1WowuHuwhXPjEUsUKHxxNEJn0E9/S4PZQ6ko5tnLDueuAes0lb84FSPU4DF9cfe3NNAR8HHGAhrh+Qmtgu6wyZYDwF39LZao6LsQTzG2sGwJ4XDPQCuxZIab8+YrVyOTUe4aCFWlUq+ZWFY4CCHeIIS4JIS4KoSwVXMhgANdQfwelyVM44tTMY70mr+4hRAM94e4MGX+RjgyEcXtEpY40HSot5npaNL0MyBX9Zpg1SjNXSqG0DbbBZnJ5rg2s2SJOak0lhQOQgg38FfAG4Fh4J1CiGFzR1VZPG4XB3uCXJo2d3FLKbk0FeNInzUW9+GeZq5ML5keizk/EeFAV7AmdYO241CP1qv68oy5a+XWvJY6Wq1aPqVwoDuIS2jlsc3k5nycVDbHYQsoEZXGksIBeAC4KqW8LqVMAZ8BHjZ5TBXnULe2EZrJ2MIyS8kMR3rNd5+AppUmMzlum5zDPjIZtYRLCVi1Xi6brEjcno/jEjDQ2mjqOEA7DLenI2D6nFya0u5fK1iYlcaqwmEAyK/hPKY/tooQ4n1CiFNCiFOzs9YqL1AsB3qCTEVXiJrYKtMwy61iFhvjuGSiaymRyjAdTbK/y3wNGbTNOOBzc9lkLflWOMFAWyM+jzW2jUM9zaZbDpemY7iEZsnYDWt8ymUgpfyYlPKklPJkV1d9Hlk/1K1thGZaD0ZvCass7v1d2jhuzJlnOYwtLAOYUk+pEEIIDvY0m+6CvDWfYHe7NQQmwP7uALfCiap1QiuGy1Mx9nQGLOF+rDRWFQ7jaOcrDAb1x2zFPl0zvWliOuvoQoKWRi8tjdY49h/we+gI+Ex1KxllGQbbrCEcQBOaN00UmAC3wwl2dVhnTna1N5HNSSYjK6aN4eZ8nH2d1lCsKo1VhcOzwEEhxF4hhA94B/CoyWOqOP2673Z0wbyb/nZ4mV0W0ZANhtqbTK2bY7z3ULv5vnWDofZGpmMrJDPmnB6PraQJx1PsttBaMSw7s9aKlJKxhWVLrZNKYknhIKXMAB8AvgpcAB6RUp43d1SVp8HrpifkX3VjmMFoOGE54bCrvclcy2FhmQaviy4Tqo5uxmBbE1LCxKI5WvJappJ11sqQbtmZtVYWE2mWkhlLWZiVxJLCAUBK+ZiU8pCUcr+U8qNmj6daDLWZpyVnc5LxhWUGLab5DLU3Mr64bJoveTScYLCtyfRzH/kMtWmf0ZhJVqaxAe+yUMyhr6UBj0uYZnkbSt1gm7Xun0phWeHgFIbam0yzHKajK6SyOUtaDmb6kkcXllc3Y6swuOpCMWetGJaDlWIOHreL/tZGbps0J4agVsJBURWG2hqZjCyTNkFLXtMGrXPDg7m+ZCklYxZ0tfWGNC3ZLMvh1nyczqCPoL92fbSLwUwX5OiC9RIXKokSDiYz2N5ETsLEYu21n9XAq8UWtzGeWybc9JHlNLFkxjJprAZul6C/tZFRk6zMW/PWE5hgbvLC2MIyoQaPZTL9Ko0SDiZjbIRmuAtGF5ZxibWsKavQ19KA2yUYN2EjND4HK2qDg22NpsYcrFA2Yz1D7Y2E4yniyUzN33tsYdmS66RSKOFgMoa/0oyg2thCgt5Qg2VOvBp43C76WhpM2QiNz8GK6Yla8kLtBWYyk2UiYr2UZ1gT4uMmWd52jTeAEg6mY2jJZmyEVtZ8BlobTQnUr51xsN68DLU3MreUZDlV27MOYwvLSGmtNFaDQZOyuIwzDla9fyqBEg4mo2VcNJiiEY4vLFtW8xlsazJHG9RPjFuxUbwhsGq9Ed624BkHgzXhUNu1Eo6nWE5nLWlhVgolHCzAUFtTzd1K6WyOyYiVhUMjU9EVUpnaZnGNhq174tXQUmu9Vm7pDXWsdMbBoCvox+9x1Vw4jC5YNzZVKZRwsABm+JKnIivkpHUX92BbI1LCZKTWN33CctlbBobQqvVauRVO0ORz0xn01fR9i0EIwYAJgXpDYFrRmqoUSjhYADN8yaMWP8AzYIK7IJczauVY84bvCvpp8Lpqnrp5W09jtdKJ8XwG22p/kNSqaeCVRAkHC2CGL3nM4maxcdPVMp11UndjWVUbFEIwaIIL8lY4Ydk5ASPFt7bC4XY4QVezn0af/Up1GyjhYAHM8CXfnIvjcQn6Whtq9p6l0NvSgNctuFHDBvLXZvTeFl3WLcE81NZYU7dSJpvj9nyCPRY842Cwu72JcDzFYiJVs/e8HU5YqkJtNVDCwQLs0bWy67O12wgvTy+xryuA123NJeB1u9jbGeBKDRvcXNMbH+23SOOjQuzuCHBrPk6uRj22b4UTpLI5Dlq4DeZa98DarBUpJVdnltjTaV2BWQmsuTM4jI6gn65mPyOTtWuNeXk6ZukbHuBgdzOXa9gl79rsEi2NXjoC1gu8GhzpbSaeytbMyjSE86Ee6wrMo31ar++LNRIOM7Ekc0sp7rJIj/FqoYSDRTjaF+LCZG0WdyKVYXQhwWGrC4eeIKMLiZoF6i9PLbG/K2DZwCusbYQjE7VRJAzhbJU2soXobvbT2uStmXA4Nx4B4K6Blpq8n1ko4WARjvY1c3UmVpO8/ktTMaTUGrRbmcM9zUgJV2aqf9PncpKRyajlb/jDvc24BFyokZV5aSrGrvYmmnzWqsaajxCCI73NXJyqzZycG48ixJqgtitKOFiE4b4Q6axc9XtXE0PzuWfQ2hvhcH/ttOSb83GWkhnLC4cGr5u9nQFGamRlnhlf5G6LzwnAkd4Ql6diNYnFnJuIsK8zQMBi5csrjRIOFqGW7oIzYxE6Aj76WqyZqWQw1NZE0O+pSSzmnD7vd/VbfyPUXJDVn5PFRIrR8DJ3W1yJAM3yrlUs5vx4xPJKRCVQwsEi7OsM4Pe4arIRntUXt5V96wAul2C4L8T5GgjMc+MRfB4XBy0ceDUY7g8xvrhMJJGu6vuc1S3MerAchvu0MVZ7rcwvJZmIrNSFErFTlHCwCB63iyN9Ic5PRKr6PivpLFdmlizvUjIY7te05Gq7C86NRzja22zZ1N58jukb0/nJ6q4VQzjUw0Z4sCeIxyWqbnkbwufYgL3jDaCEg6U41q9pyVJWbyMcmYySzcm6MYuH+0MkUlluVvEwnJSSc+MRjtXJnByrUSzm7FiE3R1NtDRZr0Ltehq8bg50B6tueZ/TlbdjdSAwd4oSDhbiWH+I2Eqmqidgz47VRzDaYNiIxVTxph9bWCa6klnddK1OZ9BPT8hfdRfKmbFIXbiUDIb7QtW3HMaj7Gpvsm1r0HyUcLAQhvleTdfS+QktGN0bsnYw2qAW7gIjP76eUhOrvRGG4ynGF5frRokAzcqciq4wv5Ss2nucm4hwlwNcSqCEg6U43NuM2yWqqhGOTEYZ7g9ZPhht4Pe4OdjTXNU5uahbJVY/95HPsf4Wrs4usZKuzgHBs3V40KvaVmZkOc2t+YQjXEpgknAQQvyJEOKiEOKMEOILQojWvOc+IoS4KoS4JIT4cTPGZxYNXjcHuoJVsxzS2RyXp5ZWb6J6YbgvVFW30sVp7aBXsI7y1o/1h8jmZNXqCV3SD5TV01qp9rkYI324XtyPO8Usy+HrwF1SynuAy8BHAIQQw8A7gGPAG4D/JYSwb03cAhzrD63m3Feaa7NLpLK5unKfgDYns7EkM7GVqlz/4mR0tXhbvWBor9USmpemlugJ+Wltsm6dqfW0NvkYaG2s2pwYdabqba2UiynCQUr5NSllRv/1KWBQ//lh4DNSyqSU8gZwFXjAjDGaxbGBlqpthIZGNVxnmk81NcKVdJYbc3GO1tkNP9jWSLPfUzUr8/J0rK7cbAZHqxiLuTy9RLPfUzfxup1ihZjDe4HH9Z8HgNG858b0xxyDYbJWw8d+YTKKz+NiX52VGj5aRV/y1ZklchIO99aXwHS5BEf7q3NAMJuTXJmJWb4wYyGG+0Ncq1Is5vJ0jAM9wbqJ1+2UqgkHIcQ3hBDnCnw9nPea3wIywKfLuP77hBCnhBCnZmdnKzl0U6mmlnxpeokDXUE8dXDQK5+WRi9D7Y1VmRMjU+lIX/1thMf6Q1ycjJGt8AHB0XCClXSuLi2H4b4QOVmd3g5XZpY41F1/c1IuVYvASSlft9XzQohfAN4MPCTXTn2NA0N5LxvUHyt0/Y8BHwM4efJkbTqf1IBQg5eB1sbqLO7pGC/d217x69aCaqVuXpyM4ve4LN3pbDOO9oZYTmcZDScq2njmktHDoc5cbXCn5X18qLVi151fShKOp+qivEqlMCtb6Q3AbwJvkVLmV8p6FHiHEMIvhNgLHASeMWOMZnK4t5nLFe6AFl1JMxlZsXyDn8042hfixny84r0dLk5pvnW3q/5cBUZgtNJ9DC5OxhACDlq4h8NmGLGYShcmNPpa1Ov9Uw5m+Rf+EmgGvi6EeFEI8TcAUsrzwCPACPAV4FellLXp9GIhDvU0c212iXS2cr0druiLux5dBaCVZJaSigvNi1Oxus0+MbTYSs/JyGSEvR31WZJaCMGRvsr3djCETb0lLuwEUz59KeWBLZ77KPDRGg7HchzuDZLOSm7OxSumqaym4dWpcDjaZ2jJlXMXzC0lmVtKcqROb/gmn4dd7U2rbqBKMTIZ5Z7B1opes5Yc6Q3xxRfGkVJWLHg8MhmlM+ijq9lfkevVA/UVmXQIhnZfyZv+8vQSDV4Xg22NFbtmLRlqa6LJ565oK1Uj06eeDnqt53Bvc0XjU9GVNKPh5bqek6N9IWLJDGMLlatRdmEyytG++qksUAmUcLAg+7uCuF2CixXcCM9NRDjaF8JVh7510FI3D/VU1l1gdMSrl2qshTjc08yNuXjFUjeNNVfPwsHIPKtU3CGdzXFluv4qC+wUJRwsSIPXzcHuIKfHFityvWxOcn48wj11vAmC5lq6OBWrWEnzc+N6Seo6rrB514BWRqNSQekR/VBdvR2UzOdwTzNCVO5cjFFZoJ7npByUcLAo9+1q5fToYkU2whtzS8RT2boqolaIY/0tLCbSFXMXnB2P1EUjm60w4i+nRxcrcr2RySjtAR/ddexbD/g97O8Krpan3ynnxuvf/VgOSjhYlOODrURXMtyc33lP3DOrPRxad3wtM7lX3whfrMBGuBBPMbawXPcCszfUQHezv2LC4cJkjGEb+NaPD7ZyeqwyytWZsUUCPjf7uuovtXcnKOFgUSqpEZ4dj9DodbO/q/4OeuVzuLcZn8fFmQq424yOXvXUzKYQQgiOD7XyYgXmJJ3NcWk6Zgv3yb1DLcwtaT0pdsrpMa1LYD2ehdkJSjhYlIPdQRq97opoyWfHIhzrD9Vd2Yz1eN0uhvtCnK6Au2CtX4EdNsJWrs/GiSynd3SdS1MxUpmcLUpSG1bymR2ulVQmx4XJKMfrqOlRpajv3cLGeNwu7h5o2XFQOpPNcX4iyt02WdzHB1s4Nx7ZcT2hc+MRhtob66ok9WYc1zfCnfrYn7kRBuAle+qzxEo+R/qa8bldO7a8L09rArPeXbLloISDhTk+1ML5iSipTPknpa/NxllOZ+uq3eNWHB9qJZHKcnVmaUfXOTNW/8FoA0Pw71SReOZGmMG2Rvpb6/MsTD5+j5uj/aEdW97GnB5XwkFhJe4daiOVye0ot//52wtA/QejDYz/Yycb4dhCgrGFZVtoyKBVrd3XFdjRRiil5NmbYR6wyZyAZmWe3aGVeWY0QluTVhXYaSjhYGGOD+ka4Q5u+h9cnaMn5K+7Hg6bsa8zQLPfs6M5efLaPAAvP9BRoVGZz72Drby4g9Tn63Nx5uMpHqjTqr2FOD6oWZlXZso/A/LMzTD37Wqr++ytclDCwcIMtDbSGfTz3K2Fsv4+l5P88No8rzjQaZvF7XIJ7tvdxtO6f7wcnrw2T0fAZ6va/MeHWpmNJcvOzlmNN9hIOBiC7odX58v6+7GFBDfm4rzyQGclh1U3KOFgYYQQvGx/Bz+4Nl+WRnhhKko4nrLd4n7lgQ6uziwxGSl9I5RSE5gP7u+o21IihXj5fs0K+t6VubL+/tkbYTqDPttYmABD7U3s7mji+1fLmxNDqLzyoL3un2JRwsHivGJ/B7OxZFkBWEMbfNl++7hPAF51sAsobyO8OZ9gKrqyupnahQPdQfpbGvj2pZmy/v6Zm2FesqfdNhamwasOdvLU9fmykjqevD5PZ9Bfl30tKoESDhbnFbrW/4MytJ+zYxG6m/30tdgrmHakt5nOoL+sOXlBD9DbJRhtoFmZnZy6uVCylTkZWbZVgD6fVx7oIpHKlnxwUkrJk9fmeXCf/QRmsSjhYHGG2psYbGvk2Zulxx3Ojkfq/gRwIYQQnNzdVlZQemRCawtqJ/eJwfGhFubjKSYjKyX9nXFQ7N5drVUYlbncp/9PxqHHYhlfXGYqumKrAH2pKOFQB9w90ML5idIWdzyZ4erskm0Ov63nWH+Im/MJYiulnQq+MBXlSG9z3Z8WL4RRJ6rUjfD8RBSX0HpS243uZj+dQd9q745iMfqG1HvtrZ1gvzvEhpSzEZ6fiCJl/dcO2oxjetmLUpr/SCkZmdCattiR4b4Qbpco+aT0yESUfV1BGn3uKo3MPIQQDPe3lCwcRiaiCEHddgmsBEo41AHH9JO8pWyEhvZoW+Ggz0kpFtVUdIWFRNoWheUK0aAXVyy1yc3IRMTW5aiP9Ye4Mh0jmSm+IdKFySh7OgI0+eqvj3alUMKhDjAKoZWyEZ4dW9TKOYcaqjUsUynHXTBig7ag23G0L1SScFiIp5iIrNii2N5mHOsPkclJrkwXn/F3YSpq63VSDEo41AHdoQY6g/6SNsJzE1FbVBzdjHLcBYZwOGLjm364L8REZIXFRKqo1xvzZ2ffurHJF6tcxVbS3JpPcLTPuS4lUMKhbjjWHyp6I0ykMlybXVp1vdiVUt0FF6ai7OloIui3r6vAiKcU2yLT2DDtbDns6QgQ8LlXlYPtuKS3XLVrbKpYlHCoE0rZCC9MxpDS3jc8lO4usHMw2mBVOBS5EZ6biDLQao/S5ZvhcgmO9hWvXBluObvGpopFCYc64Vh/S9EbodEk/piNXQVQWlB6Kam1XLW7H7mr2U9Xs7/o5IXzExHbKxGgKRIXJqPkiqjQOjIZpbXJS69N43XFooRDnWDcwOeKyGE/PxGlrclLf4u9F/fuds1FVIxGeNFB2uBwX6got1I8meHGXNz27kfQFIl4KsvN+fi2rx2ZjHG0t/77aO8UU4WDEOLXhRBSCNGp/y6EEH8hhLgqhDgjhDhh5visxK4SNsKRySjD/fZf3Jq7oLmoOXGSq+BoX4irM7Ft6wldnIo6wv0Ia5/7dmslm5Ncmoo6Yp1sh2nCQQgxBLweuJ338BuBg/rX+4C/NmFolsTlEgz3hbZ1oWiLO2bL066FONIb4tJUbNt6QiOTmjXlBFfBcH+IdFZuW6zRcD0dcUBWzoHuIG6XWA02b8aNuTgr6ZztY1PFYKbl8GfAbwL5d/XDwKekxlNAqxCiz5TRWZDh/hAXJmNbdra6NR8nmclx2CEnOw/3NrOUzGzbx8AIRtvdmgIY1jf77c47XJqK0ez3MGCDtqDb0eB1s7czwMVthIMxZ05PYwWThIMQ4mFgXEp5et1TA8Bo3u9j+mOFrvE+IcQpIcSp2dnZKo3UWhzrD7GcznJjbnO/qbH4jzjGctBu4q00wkw2x8WpmO2D0QZ7O4M0eF3bxh0uTcU41NvsCIEJ2lq5NL31nFyYjOJ1Cw7aqBFUuVRNOAghviGEOFfg62Hg/wJ+eyfXl1J+TEp5Ukp5squrqzKDtjjFZOdcnIrhEnCwxxk16A/pwmErjfDGnGZNOcWP7HYJDvdufVJaSsnFqahjLEzQhMNoeJmlZGbT14xMRtnfFcTnUbk6VZsBKeXrpJR3rf8CrgN7gdNCiJvAIPC8EKIXGAeG8i4zqD+mQNvwfW7Xljnsl6ai7OkM0OC1XxG1QoQavAy0Nm5pOYysugqcIRxAcy2NTEY3jcVMRVeIrmQcVVjOsKY3WytSSs6Nq2C0Qc3Fo5TyrJSyW0q5R0q5B811dEJKOQU8Crxbz1p6EIhIKSdrPUar4nW7ONQb3DTjQkrJ2bGIozZB0DTCrVwoL9xepMnndlRHr+G+EIuJNFPRwr0dVkuJOMT9CHBU3/TPbtL4ZzS8zNxSkvt2tdVwVNbFarbTY2iWxVXgb4FfMXc41uNYn9bboZBGOBpeZiKywksd1qDkxO42rs4sMb+ULPj8c7cWOD7YasseDpsxrLsgX7y9WPD5Z26E8bqFbav2FmKgtZGB1kaeuh4u+PzzepfAEzZselQOpt8tugUxp/8spZS/KqXcL6W8W0p5yuzxWY27B1tYSKS5NrsxKP3kda1t5sv22as/8nY8qP+/Rs/sfJaSGUYmo5zY3VrjUZnLPYMtBP0evrtJn+2nboQ5Pthqyx4OW/Hgvg6evjFf8KT0k9fmafZ7ONzjHFfbVpguHBSl8bqjPQA8fnajt+2xs1P0tzRwwEHuE1jbCJ+4OLPhuScuTJPNSX7kULcJIzMPr9vFy/Z38N3LsxuszLmlJOfGI7xsv7OUCIDXHO5iIZHmqevzdzyezub46sgUDx3tdpSFuRVqFuqM3pYGXrKnjS++OH7HTT+xuMx3r8zy9vsHHZOaaOB1u/iJu/t47Owk8XWZKF8+M0l3s5+Tu53nR37jXb2MLy7z5LqN8MunJ8jmJD95vN+kkZnHjw33EGrw8Mip0Tse/86lWRYTad50tzpWZaCEQx3yzgd2cW02zvevzvGdy7NcnIry2WdHkRLefv/Q9hewIW8/OUgileU/dIsqlckxsbjMNy/O8FMnBnC5nCUwAd50dx8tjV7++WmtCMFKOouUkn9+5jbH+kMccqD7pMHr5i339vP4uSlmYis8enqCqcgK//DDm/SGGnjtEWdZmFth38L2NuYn7unjT756iZ//xDN3PP764R52dTSZNCpzObm7jUM9Qf7mO9d4+nqYb1+aYbg/hJSSn39wt9nDM4UGr5u3nRjkU0/e5L/862m++OI4P3lPP5enl/jTnz1u9vBM4xdevpd/fvo2D3z0iTse/8gbj+BVLqVV1EzUIX6Pm//7J4ZXfxcCGrwu/usbj5g4KnMRQvAbrz/M9dk4n39+jHAixfeuzPHzD+5msM2ZAhPg/a/Zh9/j4l+fGyOdlfzbC+Mc6W12pEvJ4EB3kPe8fA8AfXrl4sG2xtXHFBpiu4Jl9cDJkyflqVPOS2w6PbrIUHsT6WyOnJT0tdi/Rs52fOrJmyTTOe7f08ZXzk3xwYcOErBx57di+OHVOb5+YZq33jvAI6dG+d9ftY+9nQGzh2UquZxkZDKqV7Bdoifkt3XDo80QQjwnpTxZ8DklHBQKhcKZbCUclFtJoVAoFBtQwkGhUCgUG1DCQaFQKBQbUMJBoVAoFBtQwkGhUCgUG1DCQaFQKBQbUMJBoVAoFBtQwkGhUCgUG7DFITghxCxwq8w/7wQKF703H6uOTY2rNNS4SkONqzR2Mq7dUsquQk/YQjjsBCHEqc1OCJqNVcemxlUaalylocZVGtUal3IrKRQKhWIDSjgoFAqFYgNKOMDHzB7AFlh1bGpcpaHGVRpqXKVRlXE5PuagUCgUio0oy0GhUCgUG1DCQaFQKBQbcIRwEEL8jBDivBAiJ4Q4ue65jwghrgohLgkhfnyTv98rhHhaf91nhRAVbxmlX/dF/eumEOLFTV53UwhxVn9dTTocCSF+Rwgxnje+N23yujfo83hVCPHhGozrT4QQF4UQZ4QQXxBCtG7yuprM2Xb/vxDCr3/OV/X1tKdaY8l7zyEhxLeEECP6PfDBAq95jRAikvf5/na1x6W/75afi9D4C32+zgghTtRgTIfz5uFFIURUCPGhda+pyXwJIf5OCDEjhDiX91i7EOLrQogr+ve2Tf72Pfprrggh3lPWAKSUtv8CjgKHgW8DJ/MeHwZOA35gL3ANcBf4+0eAd+g//w3wy1Ue7/8EfnuT524CnTWev98BfmOb17j1+dsH+PR5Ha7yuF4PePSf/wj4I7PmrJj/H/gV4G/0n98BfLYGn10fcEL/uRm4XGBcrwG+XMs1VcznArwJeBwQwIPA0zUenxuYQjsoVvP5Al4NnADO5T32x8CH9Z8/XGjNA+3Adf17m/5zW6nv7wjLQUp5QUp5qcBTDwOfkVImpZQ3gKvAA/kvEEII4EeBz+kPfRJ4a7XGqr/fzwL/Uq33qBIPAFellNellCngM2jzWzWklF+TUmb0X58CBqv5fttQzP//MNr6AW09PaR/3lVDSjkppXxe/zkGXAAGqvmeFeRh4FNS4ymgVQjRV8P3fwi4JqUst/rCjpBSfhcIr3s4fw1tthf9OPB1KWVYSrkAfB14Q6nv7wjhsAUDwGje72NsvHE6gMW8TajQayrJq4BpKeWVTZ6XwNeEEM8JId5XxXGs5wO6af93m5iyxcxlNXkvmpZZiFrMWTH//+pr9PUUQVtfNUF3Y90HPF3g6ZcJIU4LIR4XQhyr0ZC2+1zMXlPvYHMlzYz5AuiRUk7qP08BPQVeU5F585Q+NmsihPgG0Fvgqd+SUv57rcdTiCLH+E62thpeKaUcF0J0A18XQlzUNYyqjQ34a+D30G7m30Nze713p++503EZcyaE+C0gA3x6k8tUZc7qCSFEEPg88CEpZXTd08+juU6W9HjSF4GDNRiWZT8XPa74FuAjBZ42a77uQEophRBVO4tgG+EgpXxdGX82Dgzl/T6oP5bPPJo569G1vUKvqcgYhRAe4KeB+7e4xrj+fUYI8QU0d8aOb6hi508I8bfAlws8VcxcVnxcQohfAN4MPCR1h2uBa1RlztZRzP9vvGZM/6xb0NZXVRFCeNEEw6ellP+2/vl8YSGlfEwI8b+EEJ1SyqoWmSvic6nKmiqSNwLPSymn1z9h1nzpTAsh+qSUk7qLbabAa8bR4iIGg2jx1pJwulvpUeAdehbJXjTp/0z+C/QN51vA2/WH3gNUyxJ5HXBRSjlW6EkhREAI0Wz8jBaQPVfotZVknZ/3pzZ5z2eBg0LL7PKhmeSPVnlcbwB+E3iLlDKxyWtqNWfF/P+Poq0f0NbTNzcTaJVCj2l8ArggpfzTTV7Ta8Q+hBAPoO0LVRVaRX4ujwLv1rOWHgQieS6VarOpBW/GfOWRv4Y224u+CrxeCNGmu4Bfrz9WGtWOuFvhC21DGwOSwDTw1bznfgsty+QS8Ma8xx8D+vWf96EJjavAvwL+Ko3zH4D3r3usH3gsbxyn9a/zaK6VWszfPwJngTP64uxbPzb99zehZcNcq8XY9M9jFHhR//qb9eOq5ZwV+v+B/4YmvAAa9PVzVV9P+2owR69EcweeyZunNwHvN9Ya8AF9bk6jBfZfXoNxFfxc1o1LAH+lz+dZ8jINqzy2ANpm35L3WM3nC004TQJpff/6RbQY1RPAFeAbQLv+2pPAx/P+9r36OrsK/Kdy3l+Vz1AoFArFBpzuVlIoFApFAZRwUCgUCsUGlHBQKBQKxQaUcFAoFArFBpRwUCgUCsUGlHBQKMpACNEqhPiVdY89LoQws76TQlExlHBQKMqjFa3KKgBCiEagQ25ygFGhqDeUcFAoyuMPgf16Pf8/QStX8G1Y7VPwB/pzp4QQJ4QQXxVCXBNCvF9/TZ8Q4rv6a84JIV5l2n+iUBTANrWVFIoa82HgLinlvQBCiL9AK8BmcFtKea8Q4s/QTr6/Au2E9Dm0niDvQjup/1EhhBtoqt3QFYrtUcJBoagMrwB+I+93o67SWSAotV4KMSFEUmgd654F/k4vivdFKeWLtRysQrEdyq2kUOwQIcQ+YFRqTX4Mkvr3XN7Pxu8eqZWmfjVaBc1/EEK8uyaDVSiKRAkHhaI8YmhtN0Er7/yVUv5YCLEbranT3wIfR2sHqVBYBuVWUijKQEo5L4T4gdCav08Cv1TiJV4D/BchRBpYApTloLAUqiqrQrEDhBB+4AdSypNmj0WhqCRKOCgUCoViAyrmoFAoFIoNKOGgUCgUig0o4aBQKBSKDSjhoFAoFIoNKOGgUCgUig0o4aBQKBSKDfz/xCgngWwQ2Y0AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aly.autocorr(p).plot(-10,10,xlabel=\"t/ms\")    #Compute the autocorrelation function of p and intercept the part of [-10ms,10ms)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observe the autocorrelation function and we can find that although the audio p consists of superimposed components of several frequencies, the period is still about 200 samples, corresponding to a duration of about $4.54ms$, which is the period of a $220Hz$ sine wave."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(220.0, 0.0449080316623462)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aly.getMaxFrequency(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The getMaxFrequency function gets the frequency component and amplitude of the largest amplitude in the audio. It can be seen that $220Hz$ is the main frequency component in the audio."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Noise\n",
    "\n",
    "Noise is an audio signal with no apparent pitch, usually generated by random vibrations. A typical noise is **white noise**, which has the property $\\gamma(\\tau)=\\begin{cases}\\sigma^2,& \\tau=0\\\\0,& Others\\end{cases}$, i.e., the self-covariance function is equal to the variance when when the time difference $\\tau$ is 0, and the covariance is 0 at all other moments. if the white noise is consisted of i.i.d. samples from the zero-mean Gaussian distribution $N(0,\\sigma^2)$, it is called **Gaussian white noise**.\n",
    "\n",
    "When a stochastic process **any finite dimensional distribution function is only related to the time difference**, that is, if the stochastic process $\\{X(t),t\\in T\\}$ satisfies: for any $n\\in N$, any $t_1,t_2,... ,t_n\\in T$, and any h, when $t_i+h\\in T,i=1,2,... ,n$, the n-dimensional random variables $(X(t_1),X(t_2),... ,X(t_n))$ and $(X(t_1+h),X(t_2+h),... ,X(t_n+h))$** have the same distribution function, the process is a **stationary stochastic process**. The definition of stationary stochastic process is very strict, usually we use the general definition of **generalized stationary stochastic process**: **the first two order moments are independent of t and the autocorrelation function is only related to the time interval**. Gaussian white noise is also a typical generalized stationary stochastic process.\n",
    "\n",
    "For a stationary stochastic process, define the time mean of the stochastic process $X(t)$ as $<X(t)>=\\displaystyle\\lim_{T\\rightarrow ∞}\\int_{-T}^TX(t)dt$ and the time correlation function as $<X(t)X(t+\\tau)>=\\displaystyle\\lim_ {T\\rightarrow ∞}\\int_{-T}^TX(t)X(t+\\tau)dt$. If $P\\{<X(t)>=E\\{X(t)\\}=\\mu_X\\}=1$, then the mean value of the process is said to have **ergodicity**, and if $P\\{<X(t+\\tau)X(t)>=E\\{X(t+\\tau)X (t)\\}=R_X(\\tau)\\}=1$, then the self-covariance function of the process is said to have **ergodicity**. The stochastic process with ergodicity can use the time mean to estimate the expectation, and the integral over time of the self-covariance function can be used to estimate the integral over the probability density. Therefore, a long enough single realization of the stochastic process with ergodicity can be used to estimate the first and second order moments of the process.\n",
    "\n",
    "For the analog audio signal corresponding to the random process with ergodicity, we only need to represent its one realization as a digital audio signal of sufficient length, then we can estimate its mean, variance, and self-covariance functions.\n",
    "\n",
    "Noise also has energy and power, and its calculation method and meaning are the same as musical tones. For Gaussian white noise, the power is equal to the variance $\\sigma^2$.\n",
    "\n",
    "If noise is mixed with another audio signal, using the power of signal and noise we can define the signal-to-noise ratio: $snr=10log_{10}\\frac{P_{signal}}{P_{noise}}(dB)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The power of the audio:  0.00022002572458715804\n"
     ]
    }
   ],
   "source": [
    "monotone_without_wn = ak.create_Single_Freq_Audio(0.02,440,44100,1)\n",
    "monotone_with_wn = monotone_without_wn.addWgn(10)   #在单音上加上信噪比为10dB的高斯白噪音\n",
    "monotone_with_wn.sound()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "monotone_with_wn.plot(0, 0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The power of the audio:  1.9981753738607665e-05\n"
     ]
    }
   ],
   "source": [
    "wn = monotone_with_wn - monotone_without_wn #Subtract the monotone, leaving only white noise\n",
    "wn.sound()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "wn.plot(0, 0.01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-4.358634195667403e-05, 1.99798539694025e-05)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(wn.samples), np.var(wn.samples)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It can be seen that the mean value of white noise is close to 0, while the variance is equal to the power."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "aly.autocorr(wn).plot(-440,441,xlabel=\"k\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The autocorrelation function of white noise is significantly greater than 0 when and only when $k=0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Consider such a general stochastic process: $X_t=c_0+\\displaystyle \\sum_{k=1}^∞ [a_k sin(\\frac{2\\pi k}{T} t)+b_k cos(\\frac{2\\pi k}{T} t)]+\\alpha_t,-∞<t<∞$, where $\\alpha_t$ describes the random vibration, and $\\displaystyle \\sum_{k=1}^∞ [a_k sin(\\frac{2\\pi k}{T} t)+b_k cos(\\frac{2\\pi k}{T} t)]+c_0$ is the Fourier series representation of an arbitrary deterministic periodic signal, we first assume that $a_k$, $b_k$, $c _0$, $T$ are constants invariant with time, and $\\alpha_t$ is a single realization of a stationary random process. At this point the mean value of this stochastic process changes with time, so it is obviously not a stationary stochastic process. However, we can decompose the stochastic process into random and non-random parts, so that the random part is a stationary stochastic process, while the non-random part is a superposition of numerous deterministic sinusoidal signals."
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "34e3d493db18dfecee561d26c028e75a8172bde10b9fb1f75764229aafdf7eef"
  },
  "kernelspec": {
   "display_name": "Python 3.8.3 ('base')",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
